By using the substitution $\displaystyle v=x-y$, solve the differential equation $\displaystyle \frac{dy}{dx}+[1+(x-y)^2]cos^2x=sin^2x$, expressing $\displaystyle y$ in terms of $\displaystyle x$.

$\displaystyle \frac{dv}{dx}=1-\frac{dy}{dx}$

$\displaystyle 1-\frac{dv}{dx}+[1+v^2]cos^2x=sin^2x$

How do I continue to remove the x in the trigo?