Along the characteristic, the solution is constant
10
Expressão 11: "z" Subscript, "c" , Baseline left parenthesis, "s" , right parenthesis equals "z" Subscript, "c" 0 , Baselinezcs=zc0
11
Use the initial condition to determine the value
12
Expressão 13: "z" Subscript, "c" 0 , Baseline equals "g" left parenthesis, "x" Subscript, "c" 0 , Baseline , right parenthesis equals 1.9 7zc0=gxc0
equals=
1.9 71.97
13
Draw the characteristics
14
Expressão 15: left parenthesis, "x" Subscript, "c" 0 , Baseline , "y" Subscript, "c" 0 , Baseline , "z" Subscript, "c" 0 , Baseline , right parenthesis Tem gráfico.xc0,yc0,zc0
15
Expressão 16: left parenthesis, "x" Subscript, "c" , Baseline left parenthesis, "t" , right parenthesis , "y" Subscript, "c" , Baseline left parenthesis, "t" , right parenthesis , "g" left parenthesis, "x" Subscript, "c" 0 , Baseline , right parenthesis , right parenthesis Tem gráfico.xct,yct,gxc0
Domínio t mínimo: negative 6−6
less than or equal to "t" less than or equal to≤t≤
Domínio t máximo: 66
16
Expressão 17:
17
We can solve the characteristic equations to find for any point "the" initial point of "the" characteristic (there is more that one characteristic through each point)
18
Expressão 19: "x" Subscript, 0 , Baseline left parenthesis, "x" , "y" , right parenthesis equals signum left parenthesis, "x" , right parenthesis StartRoot, "x" squared minus 2 "y" , EndRootx0x,y=signxx2−2y
19
Expressão 20: "u" left parenthesis, "x" , "y" , right parenthesis equals "g" left parenthesis, "x" Subscript, 0 , Baseline left parenthesis, "x" , "y" , right parenthesis , right parenthesisux,y=gx0x,y