Math. 350-01, Fall, 2002, Text 3, problem 2

u  =  Series[y[t],  {t, 0, 4}]

Solve[{D[u, {t, 2} ] +  t*D[u, {t, 1}]  +  t*u  ==  Exp[t],  
        y[0] == 0,  y'[0] == 0}]