For nonzero constant , prove that
is a particular solution of the equation
Find the general solution of the equation
Proof. The general solution of the homogeneous equation is . Then, particular solutions of the homogeneous equation are and (taking and , respectively). The Wronskian of and is then
So, we have the functions (of Theorem 8.9) and given by
Therefore we have a particular solution of the non-homogeneous equation given by
Using this theorem, the general solution of
(where we changed the values of the constants and in the last step to absorb the extra and terms).