Show that the given differential equation is homogeneous and solve each of them.
`x^2(dy)/(dx)=x^2-2y^2+x y`

Explanation

Given differential equation is

`x^2(dy)/(dx)=x^2-2y^2+x y`

`(dy)/(dx)` = `(x^2)/ (x^2) - 2 (y^2)/(x^2) + (xy)/(x^2)`

` (dy)/(dx)`= `1 - 2(y/x)^2 + y/x......(i)`

which is homogeneous equation in the form of `f(y/x)`


put `y/x=t` => `y=xt`

diff. w.r.t. x

...