doesnt have constant coefficients?
Yes.
As long as you have (for lack of a better term) a "polynomial DE" of the form
$\displaystyle f_n(x) \frac{d^ny}{dx^n} + f_{n - 1}(x) \frac{d^{n - 1}y}{dx^{n - 1}} + f_{n - 2}(x) \frac{d^{n - 2}y}{dx^{n - 2}} + \dots + f_2(x)\frac{d^2y}{dx^2} + f_1(x) \frac{dy}{dx} + f_0(x) y = f(x)$.
In other words, as long as the coefficients are nothing more than functions of x, the equation is still linear.