1. The problem statement, all variables and given/known data y''+4y=t^2+3e^t y(0)=0 y'(0)=2 2. Relevant equations CE: r^2+4 r=+/-2i gs: y=c1 cos(2t) + c2 sin(2t) 3. The attempt at a solution guess: yp=(At^2+Bt+C)e^t yp'=At^2e^t+2Ate^t+Bte^t+Be^t+Ce^t yp''=At^2e^t+4Ate^t+Bte^t+2Ae^t+2Be^t+Ce^t back into problem: At^2e^t+4Ate^t+Bte^t+2Ae^t+2Be^t+Ce^t+4At^2e^t+4Ce^t=t^2+3e^t which becomes: 5At^2e^t=t^2 then becomes: A=e^-t/5 then 4At^et+Bte^t+4Bte^t=0 which becomes: 4A+B+4B=0, B=-(4e^-t)/25 then: 2Ae^t+2Be^t+Ce^t+4Ce^t=3e^t, e^t's cancel which becomes: 2A+2B+5C=3 ---> C=[(75e^t)-2)e^-t]/125 ok, i'm sure i'm not doing this correctly. the book answer is: 7/10sin(2t)-19/40cos2t+1/4t^2-1/8+3/5e^t what am i doing wrong? am i skipping a step?