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.