Solve the differential equation: `(x^2+y^2)dx-2xydy=0`

Explanation

`Rightarrow(x^{2}+y^{2}) d x=2 x y d y`


`Rightarrow frac{d y}{d x}=frac{x^{2}+y^{2}}{2 x y} quad ldots . text { (i) }`



Let `y=v x`


Thus, `frac{d y}{d x}=v+x frac{d v}{d x}`


Thus, `{v}+{x} frac{{dv}}{{dx}}=frac{{x}^{2}+({vx})^{2}}{2 {x}({vx})}`



`Rightarrow {v}+{x} frac{{dv}}{{dx}}=frac{1+{v}^{2}}{2 {v}} `


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