Solve the following differential equation with Laplace transform (using Inverse transform or convolution): y\'\'+4y=(t-2), y(0)=y\'(0)=0 Solution y\'\'+4y=(t-2), y(0)=y\'(0)=0 L[(t-T)] = e-Ts applying laplace transform to the given differential equation [S2Y(S)-sY(0)-Y\'(0)]+4Y(S) = e-2s (S2+4)Y(S) = e-2s Y(S)= e-2s/(S2+4) L-1[1/(S2+4)] = (1/2)SIN(2t) L-1[e-asF(S)] = F(t-a)*(t-a) SO APPLYING INVERSE LAPLACE TRANSFORMS Y(t) = (1/2)sin2(t-2)(t-2).