The given second order differential equation is
Find the general solution of the differential equation as follows.
The corresponding homogeneous equation is
The auxiliary equation of the corresponding homogeneous equation is
Obtain the roots of the auxiliary equation as follows.
Therefore, the roots of the auxiliary equation are and
Hence, the complementary solution is
Now obtain the particular solution by method of undetermined coefficients as follows.
The choice for the particular solution is
This particular solution satisfies the given differential equation.
Equate the coefficients of like terms on both sides and obtain,
(4) Solve the first two equations as shown below
Substitute in the equation and solve for B as follows.
Now from third equation , we have .
Hence the particular solution is,