Method of Variation of Parameters:

 

This method is best for a differential equation having a right-hand side containing a term for which the derivatives do not eventually become 0 or repetitive. 

Examples would be

 

We can solve the differential equation

 

 

by the following steps:

 

  1. Find the general solution yh of the homogeneous equation:

 

  1. Replace the constants in yh by variables to form yp:

 

  1. Solve the following system for

 

  1. Integrate to find

 

  1. Form the general solution: