Introduction

They take the form of

$$m(x)\frac{d^2y}{dx^2} + p(x)\frac{dy}{dx} + q(x)y = r(x)$$

$$r(x) = 0$$

$$r(x) \not= 0$$

The general solution is

$$y(x) = Ay_1(x) + By_2(x)$$

Where $y_1$ & $y_2$ are two functions of x and A & B are integration constants. We normally assume we have constant coefficients, as in driven oscillators.

$$m\frac{d^2y}{dx^2} + b\frac{dy}{dx} + ky = F_0\cos(\omega t)$$