Using laplace transforms to solve IVPplease check work thanks

[fufufu]

Homework Statement

y' - 3y = 13cos(2t)

y(0)=1

Homework Equations

y' = sY(s) - y(0)

The Attempt at a Solution

heres all my work.. i am confused as to why its not matching book solution.. i think (geussing) that I probably messing up the decomposition step..thanks for any help with this
https://docs.google.com/open?id=0BwJqUg33PgREVjdEN250WXVTaldod3NublhVc1pEdw

Homework Statement

Homework Equations

The Attempt at a Solution

sorry almost forgot to include this..book solution is:

y(t) = 4e^3t - 3cos(2t) + 2sin(2t)

 

[vela]

You made a couple of algebra mistakes, one of them due to an omission of parentheses where they were needed.

 

[fufufu]

thanks for the help..yup i see it: (As+B)(s-3) makes all the difference, giving me C=3, B=4 and A = -3...now matches book solution.. but have follow-up question..

If I start solving equation with what I think is a fully decomposed denominator, when denominator could actually be decomposed further, then the answer I get should be identical to the one solved with fully decomposed denomiator, right? so, even though i probably had to solve with more steps because deenominator wasnt fully decomposed, the answers shouls still be the same, true?

 

[vela]

Yes, you should ultimately get an equivalent answer. The two results may not be expressed in exactly the same way, but they will be equal to each other.