# Using laplace transforms to solve IVPplease check work thanks

1. Mar 12, 2012

### fufufu

1. The problem statement, all variables and given/known data
y' - 3y = 13cos(2t)

y(0)=1

2. Relevant equations
y' = sY(s) - y(0)

3. 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
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
sorry almost forgot to include this..book solution is:

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

Last edited: Mar 12, 2012
2. Mar 12, 2012

### vela

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

3. Mar 12, 2012

### 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?

4. Mar 12, 2012

### vela

Staff Emeritus
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.