Expression 15: StartFraction, "y" squared Over 2 , EndFraction equals StartFraction, 3 "x" cubed Over 3 , EndFraction plus 9 "x" plus "C" left brace, "y" greater than 0 , "y" less than 0 , right bracey22=3x33+9x+Cy>0,y<0
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Expression 16: "y" squared equals 2 "x" cubed plus 18 "x" plus 2 "C" left brace, "y" greater than 0 , "y" less than 0 , right bracey2=2x3+18x+2Cy>0,y<0
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Expression 17: "y" Subscript, 1 , Baseline equals StartRoot, 2 "x" cubed plus 18 "x" plus 2 "C" , EndRoot left brace, 2 "x" cubed plus 18 "x" plus 2 "C" greater than 0 , right bracey1=2x3+18x+2C2x3+18x+2C>0
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Expression 18: "y" Subscript, 2 , Baseline equals negative StartRoot, 2 "x" cubed plus 18 "x" plus 2 "C" , EndRoot left brace, 2 "x" cubed plus 18 "x" plus 2 "C" greater than 0 , right bracey2=−2x3+18x+2C2x3+18x+2C>0
18
Da y ≠ 0 i differentialligningen,
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er den ubrudte kurve gennem
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punktet ( 0 ; 2 ) givet ved:
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Expression 22: "y" equals StartRoot, 2 "x" cubed plus 18 "x" plus 2 "C" , EndRoot left brace, 2 "x" cubed plus 18 "x" plus 2 "C" greater than 0 , right bracey=2x3+18x+2C2x3+18x+2C>0
22
Expression 23: left brace, "x" greater than or equal to "x" Subscript, 0 , Baseline : StartRoot, 2 "x" cubed plus 18 "x" plus 2 "C" , EndRoot , right bracex≥x0:2x3+18x+2C
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Expression 24: left bracket, 2 "x" cubed plus 18 "x" Subscript, 0 , Baseline plus 2 "C" , right bracket tilde left bracket, 0 , right bracket2x30+18x0+2C~0
24
idet C for y ( 0 ) = 2 er lig med:
25
Expression 26: 2 equals StartRoot, 2 times 0 cubed plus 18 times 0 plus 2 "C" , EndRoot2=2·03+18·0+2C
