(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Solve the Initial value problem using Laplace transform

[itex]\ddot{y}[/itex] +2y = 0, y_{0}= C_{1}, [itex]\dot{y}[/itex] = C_{2}

2. Relevant equations

[s^{2}- sy(0) - y'(0)] + a[sY - y(0)] + bY

3. The attempt at a solution

s^{2}Y - sy(0) - y'(0) + 2y = 0

s^{2}Y + 2Y = sy(0) + y'(0)

(s^{2}+ 2)Y = s(C_{1}) + (C_{2})

Y = (s(C_{1}))/[s^{2}+ 2] + (C_{2})/[s^{2}+ 2]

And that is as far as I can get as I am unsure what to do now?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Solving an Initial value problem using Laplace transform

**Physics Forums | Science Articles, Homework Help, Discussion**