Set up and solve the characteristic equation for the homogeneous solution.
So the solution to the homogeneous equation is
Guess a particular solution similar to the structure of the nonhomogeneous part of the DE. Multiply the exponential term by since it is included in the homogeneous solution.
Take first and second derivatives of .
Plug these derivatives into the original problem.
so that and so the particular solution is
Finally, the general solution is