Problem 3. (40 pts) Take the Laplace transform of the following equations and find their solution in the frequency domain (s-domain), y(s). a. (10pts)dt2d2y+3dtdyy=5t(dtdy)t=0=0,y(0)=2 b. (15pts)2dt3d3ydt2d2y+3y=1+sin2t(dt2d2y)t=0=(dtdy)t=0=y(0)=0 c. (15 pts) dtdy1y1+2y2=2sint and 3dtdy1+dtdy2=y2ety1(0)=1,y2(0)=2 Hint: For parts a \& b, you can use Equation 3-10 in the textbook for the Laplace transform of higher-order derivatives