# Homework Help: Laplace Transform IVP (Easy I think)

1. Dec 7, 2013

### iRaid

1. The problem statement, all variables and given/known data
Use Laplace transforms to solve the initial value problems.
$y''+4y=0;$ $y(0)=5;$ $y'(0)=0$

2. Relevant equations

3. The attempt at a solution
$$y''+4y=0$$ $$L(y'')+L(4y)=L(0)\implies s^{2}Y(s)-sy(0)-y'(0)+4(sY(s)-y(0))=0\implies s^{2}Y(s)+4sY(s)-5s-20=0$$ $$Y(s)(s^{2}+4s)=5s+20\implies Y(s)=\frac{5}{s}$$
Now I'm supposed to take the inverse laplace of that which would just be 5. I'm not sure what to do with this now.

Last edited: Dec 7, 2013
2. Dec 7, 2013

### iRaid

Found my mistake, it's not 4y'...