Find the general solution of the equation dy/dx = (x + 4y)/(2x - y)
Divide the numerator and denominator of the right hand side by x.
The standard technique is to now make the substitution $\displaystyle y = xv \Rightarrow \frac{dy}{dx} = v + x \frac{dv}{dx}$.
You are almost certain to have an example of this technique in your class notes or textbook.