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qrious126

  • 2 years ago

how would you solve this homogeneous diff. equation?

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  1. qrious126
    • 2 years ago
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    \[x(x+y)y \prime-y(x-y)=0\]

  2. qrious126
    • 2 years ago
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    thanks @Loser66

  3. qrious126
    • 2 years ago
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    what? lol

  4. qrious126
    • 2 years ago
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    i tried substituting u = y/x

  5. qrious126
    • 2 years ago
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    im sort of messing up in the algebra part i think.

  6. qrious126
    • 2 years ago
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    i got \[(y/x)((y/2x)+1)=c\]

  7. UnkleRhaukus
    • 2 years ago
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    \[x(x+y)y'-y(x-y)=0\\y'=\frac{y(x-y)}{x(x+y)}\\\quad=\frac{y(1-y/x)}{x(1+y/x)}\]

  8. UnkleRhaukus
    • 2 years ago
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    now substitute u = y/x

  9. qrious126
    • 2 years ago
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    oh ok thanks!

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