Show that `y^2-x^2 - x y=a` is a solution of the differential equation `(x-2y)(dy)/(dx)+2x + y=0`

Explanation

`(x-2 y) frac{d y}{d x}+2 x+y=0`


Given: `y^{2}-x^{2}-x y=a`


`Rightarrow 2 y frac{d y}{d x}-2 x-y-x frac{d y}{d x}=0`


`Rightarrow(2 y-x) frac{d y}{d x}-2 x-y=0`


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


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


`Rightarrow(x-2 y) frac{d y}{d x}+2 x+y=0`


Hence, `y^{2}-x^{2}-x y=a` is the answer of the given differential equation.