Determine the general solution of the second-order differential equation
The homogeneous equation related to this is an equation of the form with and . This gives us and . So, the general solution of the homogeneous equation is given by
Then by a previous exercise (Section 8.17, Exercise #19) we know that a particular solution for the non-homogeneous equation is given by
for some constant .
Therefore, the general solution of the given equation is