Expression 30: "Y" Subscript, 3 , Baseline left parenthesis, "t" , right parenthesis equals "T" "I" Subscript, 7 , Baseline left parenthesis, "t" , 0 , StartFraction, 3 "r" to the 5th power minus 18 StartRoot, 3 , EndRoot "r" to the 4th power plus 108 "r" cubed minus 64 StartRoot, 3 , EndRoot "r" squared minus 96 "r" Subscript, 1 , Baseline plus 96 StartRoot, 3 , EndRoot Over 8 StartRoot, 3 , EndRoot left parenthesis, "r" squared minus 2 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 4 , right parenthesis left parenthesis, "r" Subscript, 1 , Baseline minus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 4 , right parenthesis , EndFraction , StartFraction, 2 Over StartRoot, 3 , EndRoot , EndFraction , StartFraction, 7 "r" to the 4th power minus 24 StartRoot, 3 , EndRoot "r" cubed plus 92 "r" squared minus 56 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 48 Over 4 left parenthesis, "r" squared minus 2 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 4 , right parenthesis left parenthesis, StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 4 , right parenthesis left parenthesis, "r" Subscript, 1 , Baseline minus StartRoot, 3 , EndRoot , right parenthesis , EndFraction , negative StartFraction, 7 "r" to the 4th power minus 24 StartRoot, 3 , EndRoot "r" cubed plus 92 "r" squared minus 56 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 48 Over 4 left parenthesis, "r" squared minus 2 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 4 , right parenthesis left parenthesis, StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 4 , right parenthesis left parenthesis, "r" Subscript, 1 , Baseline minus StartRoot, 3 , EndRoot , right parenthesis , EndFraction , negative StartFraction, 2 Over StartRoot, 3 , EndRoot , EndFraction , negative StartFraction, 3 "r" to the 5th power minus 18 StartRoot, 3 , EndRoot "r" to the 4th power plus 108 "r" cubed minus 64 StartRoot, 3 , EndRoot "r" squared minus 96 "r" Subscript, 1 , Baseline plus 96 StartRoot, 3 , EndRoot Over 8 StartRoot, 3 , EndRoot left parenthesis, "r" squared minus 2 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 4 , right parenthesis left parenthesis, "r" Subscript, 1 , Baseline minus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 4 , right parenthesis , EndFraction , right parenthesisY3t=TI7t,0,3r51−183r41+108r31−643r21−96r1+96383r21−23r1+4r1−33r1−4,23,7r41−243r31+92r21−563r1+484r21−23r1+43r1−4r1−3,−7r41−243r31+92r21−563r1+484r21−23r1+43r1−4r1−3,−23,−3r51−183r41+108r31−643r21−96r1+96383r21−23r1+4r1−33r1−4
30
Expression 31: left parenthesis, "X" left parenthesis, 4 , 1 half , 0 , right parenthesis plus "X" Subscript, 3 , Baseline left parenthesis, "t" , right parenthesis , "Y" left parenthesis, 4 StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , 0 , 0 , right parenthesis plus "Y" Subscript, 3 , Baseline left parenthesis, "t" , right parenthesis , right parenthesisX4,12,0+X3t,Y432,0,0+Y3t
31
Expression 32: left parenthesis, "X" left parenthesis, 4 , 1 half , 0 , right parenthesis minus StartFraction, "X" Subscript, 3 , Baseline left parenthesis, "t" , right parenthesis plus StartRoot, 3 , EndRoot "Y" Subscript, 3 , Baseline left parenthesis, "t" , right parenthesis Over 2 , EndFraction plus 4 , "Y" left parenthesis, 4 StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , 0 , 0 , right parenthesis plus StartFraction, "Y" Subscript, 3 , Baseline left parenthesis, "t" , right parenthesis minus StartRoot, 3 , EndRoot "X" Subscript, 3 , Baseline left parenthesis, "t" , right parenthesis Over 2 , EndFraction , right parenthesisX4,12,0−X3t+3Y3t2+4,Y432,0,0+Y3t−3X3t2
32
Expression 33: left parenthesis, "X" left parenthesis, 4 , 1 half , 0 , right parenthesis minus StartFraction, "X" Subscript, 3 , Baseline left parenthesis, "t" , right parenthesis plus StartRoot, 3 , EndRoot "Y" Subscript, 3 , Baseline left parenthesis, "t" , right parenthesis Over 2 , EndFraction plus 4 , "Y" left parenthesis, 4 StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , 0 , 0 , right parenthesis minus StartFraction, "Y" Subscript, 3 , Baseline left parenthesis, "t" , right parenthesis minus StartRoot, 3 , EndRoot "X" Subscript, 3 , Baseline left parenthesis, "t" , right parenthesis Over 2 , EndFraction , right parenthesisX4,12,0−X3t+3Y3t2+4,Y432,0,0−Y3t−3X3t2
33
Expression 34: left parenthesis, "X" left parenthesis, 4 , 1 half , 0 , right parenthesis plus left parenthesis, "T" minus 1 , right parenthesis StartFraction, 2 "r" Subscript, 1 , Baseline Over StartRoot, 3 , EndRoot , EndFraction "I" Subscript, 3 , Baseline left parenthesis, "t" , 1 , negative 1 half , negative 1 half , right parenthesis , "Y" left parenthesis, 4 StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , 0 , 0 , right parenthesis plus left parenthesis, "T" minus 1 , right parenthesis StartFraction, 2 "r" Subscript, 1 , Baseline Over StartRoot, 3 , EndRoot , EndFraction "I" Subscript, 3 , Baseline left parenthesis, "t" , 0 , StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , negative StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , right parenthesis , right parenthesisX4,12,0+T−12r13I3t,1,−12,−12,Y432,0,0+T−12r13I3t,0,32,−32
34
Expression 35: left parenthesis, "X" left parenthesis, 4 , 1 half , 0 , right parenthesis plus 2 plus left parenthesis, "T" minus 1 , right parenthesis StartFraction, 2 Over StartRoot, 3 , EndRoot , EndFraction StartRoot, left parenthesis, "r" Subscript, 1 , Baseline StartFraction, 2 "r" to the 6th power minus 8 StartRoot, 3 , EndRoot "r" to the 5th power plus 47 "r" to the 4th power minus 54 StartRoot, 3 , EndRoot "r" cubed plus 76 "r" squared plus 32 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 96 Over 2 "r" to the 6th power minus 19 StartRoot, 3 , EndRoot "r" to the 5th power plus 170 "r" to the 4th power minus 4 left parenthesis, 51 StartRoot, 3 , EndRoot "r" cubed minus 40 "r" squared minus 56 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 96 , right parenthesis , EndFraction , right parenthesis squared plus 1 , EndRoot left parenthesis, "I" Subscript, 3 , Baseline left parenthesis, "t" , 1 , negative 1 half , negative 1 half , right parenthesis cos left parenthesis, "a" Subscript, 2 , Baseline , right parenthesis minus "I" Subscript, 3 , Baseline left parenthesis, "t" , 0 , StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , negative StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , right parenthesis sin left parenthesis, "a" Subscript, 2 , Baseline , right parenthesis , right parenthesis , "Y" left parenthesis, 4 StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , 0 , 0 , right parenthesis plus StartFraction, 2 Over StartRoot, 3 , EndRoot , EndFraction plus left parenthesis, "T" minus 1 , right parenthesis StartFraction, 2 Over StartRoot, 3 , EndRoot , EndFraction StartRoot, left parenthesis, "r" Subscript, 1 , Baseline StartFraction, 2 "r" to the 6th power minus 8 StartRoot, 3 , EndRoot "r" to the 5th power plus 47 "r" to the 4th power minus 54 StartRoot, 3 , EndRoot "r" cubed plus 76 "r" squared plus 32 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 96 Over 2 "r" to the 6th power minus 19 StartRoot, 3 , EndRoot "r" to the 5th power plus 170 "r" to the 4th power minus 4 left parenthesis, 51 StartRoot, 3 , EndRoot "r" cubed minus 40 "r" squared minus 56 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 96 , right parenthesis , EndFraction , right parenthesis squared plus 1 , EndRoot left parenthesis, "I" Subscript, 3 , Baseline left parenthesis, "t" , 0 , StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , negative StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , right parenthesis cos left parenthesis, "a" Subscript, 2 , Baseline , right parenthesis plus "I" Subscript, 3 , Baseline left parenthesis, "t" , 1 , negative 1 half , negative 1 half , right parenthesis sin left parenthesis, "a" Subscript, 2 , Baseline , right parenthesis , right parenthesis , right parenthesisX4,12,0+2+T−123r12r61−83r51+47r41−543r31+76r21+323r1−962r61−193r51+170r41−4513r31−40r21−563r1+962+1I3t,1,−12,−12cosa2−I3t,0,32,−32sina2,Y432,0,0+23+T−123r12r61−83r51+47r41−543r31+76r21+323r1−962r61−193r51+170r41−4513r31−40r21−563r1+962+1I3t,0,32,−32cosa2+I3t,1,−12,−12sina2
35
Expression 36: left parenthesis, "X" left parenthesis, 4 , 1 half , 0 , right parenthesis plus 2 plus left parenthesis, "T" minus 1 , right parenthesis StartFraction, 2 Over StartRoot, 3 , EndRoot , EndFraction StartRoot, left parenthesis, "r" Subscript, 1 , Baseline StartFraction, 2 "r" to the 6th power minus 8 StartRoot, 3 , EndRoot "r" to the 5th power plus 47 "r" to the 4th power minus 54 StartRoot, 3 , EndRoot "r" cubed plus 76 "r" squared plus 32 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 96 Over 2 "r" to the 6th power minus 19 StartRoot, 3 , EndRoot "r" to the 5th power plus 170 "r" to the 4th power minus 4 left parenthesis, 51 StartRoot, 3 , EndRoot "r" cubed minus 40 "r" squared minus 56 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 96 , right parenthesis , EndFraction , right parenthesis squared plus 1 , EndRoot left parenthesis, "I" Subscript, 3 , Baseline left parenthesis, "t" , 1 , negative 1 half , negative 1 half , right parenthesis cos left parenthesis, "a" Subscript, 2 , Baseline , right parenthesis minus "I" Subscript, 3 , Baseline left parenthesis, "t" , 0 , StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , negative StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , right parenthesis sin left parenthesis, "a" Subscript, 2 , Baseline , right parenthesis , right parenthesis , "Y" left parenthesis, 4 StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , 0 , 0 , right parenthesis plus StartFraction, 4 Over StartRoot, 3 , EndRoot , EndFraction minus left parenthesis, "T" minus 1 , right parenthesis StartFraction, 2 Over StartRoot, 3 , EndRoot , EndFraction StartRoot, left parenthesis, "r" Subscript, 1 , Baseline StartFraction, 2 "r" to the 6th power minus 8 StartRoot, 3 , EndRoot "r" to the 5th power plus 47 "r" to the 4th power minus 54 StartRoot, 3 , EndRoot "r" cubed plus 76 "r" squared plus 32 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 96 Over 2 "r" to the 6th power minus 19 StartRoot, 3 , EndRoot "r" to the 5th power plus 170 "r" to the 4th power minus 4 left parenthesis, 51 StartRoot, 3 , EndRoot "r" cubed minus 40 "r" squared minus 56 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 96 , right parenthesis , EndFraction , right parenthesis squared plus 1 , EndRoot left parenthesis, "I" Subscript, 3 , Baseline left parenthesis, "t" , 0 , StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , negative StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , right parenthesis cos left parenthesis, "a" Subscript, 2 , Baseline , right parenthesis plus "I" Subscript, 3 , Baseline left parenthesis, "t" , 1 , negative 1 half , negative 1 half , right parenthesis sin left parenthesis, "a" Subscript, 2 , Baseline , right parenthesis , right parenthesis minus StartFraction, 6 Over StartRoot, 3 , EndRoot , EndFraction , right parenthesisX4,12,0+2+T−123r12r61−83r51+47r41−543r31+76r21+323r1−962r61−193r51+170r41−4513r31−40r21−563r1+962+1I3t,1,−12,−12cosa2−I3t,0,32,−32sina2,Y432,0,0+43−T−123r12r61−83r51+47r41−543r31+76r21+323r1−962r61−193r51+170r41−4513r31−40r21−563r1+962+1I3t,0,32,−32cosa2+I3t,1,−12,−12sina2−63
36
Expression 37: "X" Subscript, 4 , Baseline left parenthesis, "t" , right parenthesis equals "I" Subscript, 3 , Baseline left parenthesis, "t" , "T" StartFraction, StartRoot, 3 , EndRoot "r" to the 4th power minus 8 "r" cubed minus 12 StartRoot, 3 , EndRoot "r" squared plus 104 "r" Subscript, 1 , Baseline minus 48 StartRoot, 3 , EndRoot Over 2 StartRoot, 3 , EndRoot left parenthesis, "r" squared minus 4 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 8 , right parenthesis left parenthesis, StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 4 , right parenthesis , EndFraction plus left parenthesis, 1 minus "T" , right parenthesis StartFraction, 4 left parenthesis, "r" Subscript, 1 , Baseline minus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "r" to the 6th power minus 4 StartRoot, 3 , EndRoot "r" to the 5th power plus 40 "r" to the 4th power minus 72 StartRoot, 3 , EndRoot "r" cubed plus 128 "r" squared plus 64 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 192 , right parenthesis Over negative 2 StartRoot, 3 , EndRoot "r" to the 6th power plus 57 "r" to the 5th power minus 170 StartRoot, 3 , EndRoot "r" to the 4th power plus 4 left parenthesis, 153 "r" cubed minus 40 StartRoot, 3 , EndRoot "r" squared minus 168 "r" Subscript, 1 , Baseline plus 96 StartRoot, 3 , EndRoot , right parenthesis , EndFraction , "T" StartFraction, 3 StartRoot, 3 , EndRoot "r" to the 4th power minus 32 "r" cubed minus 48 StartRoot, 3 , EndRoot "r" squared plus 416 "r" Subscript, 1 , Baseline minus 192 StartRoot, 3 , EndRoot Over 8 StartRoot, 3 , EndRoot left parenthesis, StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 4 , right parenthesis left parenthesis, "r" squared minus 4 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 8 , right parenthesis , EndFraction minus left parenthesis, "T" minus 1 , right parenthesis StartFraction, "r" Subscript, 1 , Baseline Over StartRoot, 3 , EndRoot , EndFraction , "T" StartFraction, 3 StartRoot, 3 , EndRoot "r" to the 4th power minus 32 "r" cubed minus 48 StartRoot, 3 , EndRoot "r" squared plus 416 "r" Subscript, 1 , Baseline minus 192 StartRoot, 3 , EndRoot Over 8 StartRoot, 3 , EndRoot left parenthesis, StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 4 , right parenthesis left parenthesis, "r" squared minus 4 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 8 , right parenthesis , EndFraction minus left parenthesis, "T" minus 1 , right parenthesis StartFraction, "r" Subscript, 1 , Baseline Over StartRoot, 3 , EndRoot , EndFraction , right parenthesisX4t=I3t,T3r41−8r31−123r21+104r1−48323r21−43r1+83r1−4+1−T4r1−3r61−43r51+40r41−723r31+128r21+643r1−192−23r61+57r51−1703r41+4153r31−403r21−168r1+963,T33r41−32r31−483r21+416r1−1923833r1−4r21−43r1+8−T−1r13,T33r41−32r31−483r21+416r1−1923833r1−4r21−43r1+8−T−1r13
37
Expression 38: "Y" Subscript, 4 , Baseline left parenthesis, "t" , right parenthesis equals "I" Subscript, 3 , Baseline left parenthesis, "t" , 0 , negative 1 , 1 , right parenthesis left parenthesis, StartFraction, "T" StartRoot, 3 , EndRoot "r" to the 4th power Over 8 left parenthesis, StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 4 , right parenthesis left parenthesis, "r" squared minus 4 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 8 , right parenthesis , EndFraction plus left parenthesis, "T" minus 1 , right parenthesis "r" Subscript, 1 , Baseline , right parenthesisY4t=I3t,0,−1,1T3r4183r1−4r21−43r1+8+T−1r1
38
Expression 39: left parenthesis, "X" left parenthesis, 4 , 1 half , 0 , right parenthesis plus "X" Subscript, 4 , Baseline left parenthesis, "t" , right parenthesis , "Y" left parenthesis, 4 StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , 0 , 0 , right parenthesis plus "Y" Subscript, 4 , Baseline left parenthesis, "t" , right parenthesis , right parenthesisX4,12,0+X4t,Y432,0,0+Y4t
39
Expression 40: left parenthesis, "X" left parenthesis, 4 , 1 half , 0 , right parenthesis minus StartFraction, "X" Subscript, 4 , Baseline left parenthesis, "t" , right parenthesis plus StartRoot, 3 , EndRoot "Y" Subscript, 4 , Baseline left parenthesis, "t" , right parenthesis Over 2 , EndFraction plus 4 , "Y" left parenthesis, 4 StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , 0 , 0 , right parenthesis plus StartFraction, "Y" Subscript, 4 , Baseline left parenthesis, "t" , right parenthesis minus StartRoot, 3 , EndRoot "X" Subscript, 4 , Baseline left parenthesis, "t" , right parenthesis Over 2 , EndFraction , right parenthesisX4,12,0−X4t+3Y4t2+4,Y432,0,0+Y4t−3X4t2
40
Expression 41: left parenthesis, "X" left parenthesis, 4 , 1 half , 0 , right parenthesis minus StartFraction, "X" Subscript, 4 , Baseline left parenthesis, "t" , right parenthesis plus StartRoot, 3 , EndRoot "Y" Subscript, 4 , Baseline left parenthesis, "t" , right parenthesis Over 2 , EndFraction plus 4 , "Y" left parenthesis, 4 StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , 0 , 0 , right parenthesis minus StartFraction, "Y" Subscript, 4 , Baseline left parenthesis, "t" , right parenthesis minus StartRoot, 3 , EndRoot "X" Subscript, 4 , Baseline left parenthesis, "t" , right parenthesis Over 2 , EndFraction , right parenthesisX4,12,0−X4t+3Y4t2+4,Y432,0,0−Y4t−3X4t2
41
Expression 42: "X" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis equals "I" Subscript, 3 , Baseline left parenthesis, "t" , negative "T" StartFraction, 3 "r" to the 4th power minus 8 StartRoot, 3 , EndRoot "r" cubed plus 12 "r" squared plus 40 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 144 Over 12 left parenthesis, StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 4 , right parenthesis left parenthesis, "r" squared minus 2 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 4 , right parenthesis , EndFraction plus left parenthesis, "T" minus 1 , right parenthesis StartFraction, 2 "r" Subscript, 1 , Baseline Over StartRoot, 3 , EndRoot , EndFraction , negative "T" StartFraction, 3 "r" to the 4th power minus 56 StartRoot, 3 , EndRoot "r" cubed plus 492 "r" squared minus 536 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 624 Over 12 left parenthesis, "r" squared minus 2 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 4 , right parenthesis left parenthesis, StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 4 , right parenthesis , EndFraction plus left parenthesis, 1 minus "T" , right parenthesis StartFraction, 4 left parenthesis, "r" Subscript, 1 , Baseline minus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "r" to the 6th power minus 4 StartRoot, 3 , EndRoot "r" to the 5th power plus 40 "r" to the 4th power minus 72 StartRoot, 3 , EndRoot "r" cubed plus 128 "r" squared plus 64 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 192 , right parenthesis Over negative 2 StartRoot, 3 , EndRoot "r" to the 6th power plus 57 "r" to the 5th power minus 170 StartRoot, 3 , EndRoot "r" to the 4th power plus 4 left parenthesis, 153 "r" cubed minus 40 StartRoot, 3 , EndRoot "r" squared minus 168 "r" Subscript, 1 , Baseline plus 96 StartRoot, 3 , EndRoot , right parenthesis , EndFraction minus 4 , negative "T" StartFraction, StartRoot, 3 , EndRoot "r" to the 5th power minus 11 "r" to the 4th power plus 12 StartRoot, 3 , EndRoot "r" cubed plus 28 "r" squared minus 88 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 144 Over 4 StartRoot, 3 , EndRoot left parenthesis, "r" squared minus 2 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 4 , right parenthesis left parenthesis, "r" Subscript, 1 , Baseline minus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 4 , right parenthesis , EndFraction minus left parenthesis, 1 minus "T" , right parenthesis StartFraction, 2 left parenthesis, "r" Subscript, 1 , Baseline minus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "r" to the 6th power minus 4 StartRoot, 3 , EndRoot "r" to the 5th power plus 40 "r" to the 4th power minus 72 StartRoot, 3 , EndRoot "r" cubed plus 128 "r" squared plus 64 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 192 , right parenthesis Over negative 2 StartRoot, 3 , EndRoot "r" to the 6th power plus 57 "r" to the 5th power minus 170 StartRoot, 3 , EndRoot "r" to the 4th power plus 4 left parenthesis, 153 "r" cubed minus 40 StartRoot, 3 , EndRoot "r" squared minus 168 "r" Subscript, 1 , Baseline plus 96 StartRoot, 3 , EndRoot , right parenthesis , EndFraction , right parenthesisX5t=I3t,−T3r41−83r31+12r21+403r1−144123r1−4r21−23r1+4+T−12r13,−T3r41−563r31+492r21−5363r1+62412r21−23r1+43r1−4+1−T4r1−3r61−43r51+40r41−723r31+128r21+643r1−192−23r61+57r51−1703r41+4153r31−403r21−168r1+963−4,−T3r51−11r41+123r31+28r21−883r1+14443r21−23r1+4r1−33r1−4−1−T2r1−3r61−43r51+40r41−723r31+128r21+643r1−192−23r61+57r51−1703r41+4153r31−403r21−168r1+963
42
Expression 43: "Y" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis equals "T" StartFraction, 7 "r" to the 4th power minus 24 StartRoot, 3 , EndRoot "r" cubed plus 92 "r" squared minus 56 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 48 Over 4 left parenthesis, "r" squared minus 2 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 4 , right parenthesis left parenthesis, "r" Subscript, 1 , Baseline minus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 4 , right parenthesis , EndFraction plus "I" Subscript, 3 , Baseline left parenthesis, "t" , 0 , 0 , 1 , right parenthesis left parenthesis, 1 minus "T" , right parenthesis StartFraction, 2 left parenthesis, "r" Subscript, 1 , Baseline minus StartRoot, 3 , EndRoot , right parenthesis left parenthesis, "r" to the 6th power minus 4 StartRoot, 3 , EndRoot "r" to the 5th power plus 40 "r" to the 4th power minus 72 StartRoot, 3 , EndRoot "r" cubed plus 128 "r" squared plus 64 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline minus 192 , right parenthesis Over negative 2 "r" to the 6th power plus 19 StartRoot, 3 , EndRoot "r" to the 5th power minus 170 "r" to the 4th power plus 4 left parenthesis, 51 StartRoot, 3 , EndRoot "r" cubed minus 40 "r" squared minus 56 StartRoot, 3 , EndRoot "r" Subscript, 1 , Baseline plus 96 , right parenthesis , EndFractionY5t=T7r41−243r31+92r21−563r1+484r21−23r1+4r1−33r1−4+I3t,0,0,11−T2r1−3r61−43r51+40r41−723r31+128r21+643r1−192−2r61+193r51−170r41+4513r31−40r21−563r1+96
43
Expression 44: left parenthesis, "X" left parenthesis, 4 , 1 half , 0 , right parenthesis plus "X" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis plus 4 , "Y" left parenthesis, 4 StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , 0 , 0 , right parenthesis plus "Y" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis , right parenthesisX4,12,0+X5t+4,Y432,0,0+Y5t
44
Expression 45: left parenthesis, "X" left parenthesis, 4 , 1 half , 0 , right parenthesis plus "X" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis plus 4 , "Y" left parenthesis, 4 StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , 0 , 0 , right parenthesis minus "Y" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis , right parenthesisX4,12,0+X5t+4,Y432,0,0−Y5t
45
Expression 46: left parenthesis, "X" left parenthesis, 4 , 1 half , 0 , right parenthesis minus StartFraction, "X" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis plus StartRoot, 3 , EndRoot "Y" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis Over 2 , EndFraction , "Y" left parenthesis, 4 StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , 0 , 0 , right parenthesis plus StartFraction, "Y" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis minus StartRoot, 3 , EndRoot "X" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis Over 2 , EndFraction , right parenthesisX4,12,0−X5t+3Y5t2,Y432,0,0+Y5t−3X5t2
46
Expression 47: left parenthesis, "X" left parenthesis, 4 , 1 half , 0 , right parenthesis minus StartFraction, "X" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis plus StartRoot, 3 , EndRoot "Y" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis Over 2 , EndFraction plus 4 , "Y" left parenthesis, 4 StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , 0 , 0 , right parenthesis minus StartFraction, "Y" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis minus StartRoot, 3 , EndRoot "X" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis Over 2 , EndFraction , right parenthesisX4,12,0−X5t+3Y5t2+4,Y432,0,0−Y5t−3X5t2
47
Expression 48: left parenthesis, "X" left parenthesis, 4 , 1 half , 0 , right parenthesis minus StartFraction, "X" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis minus StartRoot, 3 , EndRoot "Y" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis Over 2 , EndFraction , "Y" left parenthesis, 4 StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , 0 , 0 , right parenthesis plus StartFraction, "Y" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis plus StartRoot, 3 , EndRoot "X" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis Over 2 , EndFraction , right parenthesisX4,12,0−X5t−3Y5t2,Y432,0,0+Y5t+3X5t2
48
Expression 49: left parenthesis, "X" left parenthesis, 4 , 1 half , 0 , right parenthesis minus StartFraction, "X" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis minus StartRoot, 3 , EndRoot "Y" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis Over 2 , EndFraction , "Y" left parenthesis, 4 StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , 0 , 0 , right parenthesis minus StartFraction, "Y" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis plus StartRoot, 3 , EndRoot "X" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis Over 2 , EndFraction , right parenthesisX4,12,0−X5t−3Y5t2,Y432,0,0−Y5t+3X5t2