Solving Initial Value Problems with Mathematica's Solver
(continued from last page...)
Your interaction should have gone like this:
DSolve[{y''[x]-3y'[x]-10y[x]==E^x, y[0]==0, y'[0]==1}, y[x], x]
So it can do non-homogeneous differential equations too. (Well, at least that one.)
Moving on....