Solve the homogeneous equation .

It has characteristic equation , which has solution .

From this, we can determine that the solution to the homogeneous DE is . This is also the entire solution when .

Now for the nonhomogeneous solution, i.e. when , we try . This would mean and .

Substituting into the DE gives

.

So the particular solution is .

Therefore when , the solution of the DE is .

Now you will need to use your boundary conditions to evaluate A and B.