Solving the differential equation $\frac{dy}{dx}=\frac{3x+4y+7}{x-2y-11}$ How do we solve the differential equation $$\frac{dy}{dx}=\frac{3x+4y+7}{x-2y-11}$$?
I tried substituting $v=yx$ but I do not seem to be getting anywhere.Putting $u=x-2y$ yielded nothing better.
Thanks!

A hint: Introduce new variables $X$, $Y$ via
$$x:=X+\alpha, \quad y:=Y+\beta$$
and choose the constants $\alpha$, $\beta$ such that the $7$ and the $-11$ on the right side of your equation disappear. In terms of the new variables your equation now has the form
$$Y'={3X+4Y\over X-2Y} ={3+4{Y\over X}\over 1-2{Y\over X}}\ .$$
This is a standard type of ODE, sometimes called "homogeneous".
