The solution of the differential equation `(dy)/(dx)=(x^2+x y+y^2)/(x^2),` is a. `tan^(-1)(x/y)=logy+C` b. `tan^(-1)(y/x)=logx+C` c. `tan^(-1)(x/y)=logx+C` d. `tan^(-1)(y/x)=logy+C`

Explanation

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


Use `y=v x`


By Differentiating with respect to x, we obtain

`

Rightarrow frac{d y}{d x}=v+x frac{d v}{d x}`

`


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

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