So the question is an initial value problem involving a second order dif eq and we need to then use inverse Laplace.

y''+4y= cost y(0)=1 and y'(0)=0

expanding,

Then solve for Y(s)

the term on the right gives us cos2t

for the term on the left I used Partial fractions. our professor doesn't want us to solve for A,B,C etc. he just wants the functions. So following his example in class I did the following:

Using the table I got

The answer in the back of the book is

Can anyone tell me what I'm doing wrong? I basically did EXACTLY what he did in class.

Thanks so much!