Solve the following differential equations: `[xsqrt(x^2+y^2)-y^2]dx + x y \ dy=0`

Explanation

We have,



`{[x sqrt{x^{2}+y^{2}}-y^{2}] d x+x y d y=0}`


`frac{d y}{d x}=frac{y^{2}-x sqrt{x^{2}+y^{2}}}{x y}`



This is a homogeneous differential equation. Putting `y=v x` and `frac{d y}{d x}=v+x frac{d v}{d x}`, we get



`v+x frac{d v}{d x}=frac{v^{2} x^{2}-x sqrt{x^{2}}}{v x^{2}} `


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