In this video I give a worked example of the general solution for the second order linear differential equation of the form

General solutions of the form:

  • a\dfrac{{{d^2}y}}{{d{x^2}}} + b\dfrac{{dy}}{{dx}} + cy = f\left( x \right) \\ \\ \\ \text{where } f(x) \text{ is of the form } ke^{px}

In this example I show you how to find the general solution to

  1. \dfrac{{{d^2}y}}{{d{x^2}}} + 2\dfrac{{dy}}{{dx}} - 3y = {e^{2x}}\hphantom{aa}{\text{    given the C.F. is }}\hphantom{a}A{e^{ - 3x}} + B{e^x}