shouldn't Y(s) be +s/(s^2+4) rather than minus. You add s to the other side not subtract it.
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!