1. The problem statement, all variables and given/known data Solve: ty''+2y'+y=tJ₂(2√t) with y(0)=y'(0)=0 2. Relevant equations 3. The attempt at a solution Applying the laplace transform i get: L(y)=Y L(2y')=2sY L(ty'')=-2sY-s^2Y Putting this together: -2sY+2sY+Y-s^2(dy/ds)=[e^-(1/s)]/s^3 Y'-(1/s^2)Y=[e^-(1/s)]/s^3 Which i can solve because it is first ordre non homogeneous> solving i get: Y(s)=[e^-(1/s)]/(4s^4 ) +Ce^-(1/s) I am stuck on how to aplly the initial value theorm. That is the limit as t approches zero of f(t) is equal to the limit as f(s)*s approaches infinity. Apllying this rule i get: [e^-(1/s)]/(4s^3 ) +sCe^-(1/s) and as s approches infinity this approaches infinity not zero. So what do i do now? to get the right solution?