Solve the homogeneous equation first. ie solve:
This can be done using the auxiliay equation method.
Next, you will need to choose a complimentary function. I would try something like , but these questions have a habit of being a little tricky. You may need to modify this =S
Finally, you can just substitute the given values back into the equation. For you will have to differentiate your general solution.
Normally,the two initial conditions give two simultaneous equations for A and B.
Two simultaneous equations and two unknowns ftw!
Anyway, post back how you get on.