Solve the following differential equations: `x y(dy)/(dx)=x^2+y^2`

Explanation

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




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



substitute `{y}={vx} rightarrow frac{{dy}}{{dx}}={x} frac{{dv}}{{dx}}+{v}`



`x frac{d v}{d x}+v=frac{x^{2}+2(v x)^{2}}{x(v x)}`


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