You can solve a differential equation in a number of ways. The two most effective techniques you can use are the method of undetermined coefficients and the power series method.

The method of undetermined coefficients is a useful way to solve differential equations. To apply this method, simply plug a solution that uses unknown constant coefficients into the differential equation and then solve for those coefficients by using the specified initial conditions.

Power series are another tool in your differential equation solving toolkit. You can substitute a power series such as the following into a differential equation:

Then all you have to do is find a recurrence relation that gives you the coefficient an.