Hello, jordanrs!

You already found the homogeneous solution: .Find a solution to the following differential equation:

. .

We can conjecture that the particular solution has the form:

. .

. .

Add the equations: .

This is supposed to equal

. . So we have: .

Equate the coefficients: .

. . and we get: .

Hence, the particular solution is: .

So far, the solution is: .

Since , we have: .

Therefore, the solution is: .