Non-linear differential equation example

Question

I'm dealing with the following differential equation

$\frac{dy}{dx} = \frac{(y-x)(a-by)}{(1-\frac{b}{a}x)(a-2by+bx)}$ with $x,y \in [0, \frac{a}{b}]$

Can anyone help me with the non trivial solution?

Thanks.

Answer 1

To your question : "whether my solution is correct or not ?" the answer is obviously NO.

Putting your solution $$y(x)= \frac{a}{2b} +\frac{x}{2}$$ into $$\frac{dy}{dx} = \frac{(y-x)(a-by)}{(1-\frac{b}{a}x)(a-2by+bx)}$$ shows $$(a-2by+bx)=0$$ at denominator.