this is a second order differential equation with constant coefficients. we proceed by assuming a solution of and then forming the characteristic equation. which in this case is:

(do you see why?)

now solve for the two roots of this equation, and . your general solution is of the form

for the particular solution (we want to know what A and B are): you know that and , we can use these equations to solve for the (constant) unknowns and to obtain our particular solution

can you continue?