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The solution of the differential equation $\left(x^2+y^2\right) d x=2 x y d y$ is
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The correct answer is:
$x=c\left(x^2-y^2\right)$
It can be written in the form of homogeneous equation $\frac{d y}{d x}=\frac{x^2+y^2}{2 x y}$
Now solve it by putting $y=v x$ and $\frac{d y}{d x}=v+x \frac{d v}{d x}$
Now solve it by putting $y=v x$ and $\frac{d y}{d x}=v+x \frac{d v}{d x}$
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