qrious126
how would you solve this homogeneous diff. equation?



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qrious126
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\[x(x+y)y \primey(xy)=0\]

qrious126
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thanks @Loser66

qrious126
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what? lol

qrious126
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i tried substituting u = y/x

qrious126
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im sort of messing up in the algebra part i think.

qrious126
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i got \[(y/x)((y/2x)+1)=c\]

UnkleRhaukus
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\[x(x+y)y'y(xy)=0\\y'=\frac{y(xy)}{x(x+y)}\\\quad=\frac{y(1y/x)}{x(1+y/x)}\]

UnkleRhaukus
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now substitute u = y/x

qrious126
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oh ok thanks!