# Laplace Transform

1. Feb 11, 2009

### Kleanthis

Hello from Greece!Gongrats for your forum.

I was wondering if anyone could give me a hand with this initial value problem.
It s to be solved via Laplace transform.

y''(x)-xy'(x)+y(x)=5 , y(0)=5 and y'(0)=3

Applying the transform to the given equation I end up to :

sY'(s)+(s^2+2)Y(s)=5/s^2 + 5s + 3

This is a non linear first order differential equation with the variable s.

Any ideas to continue?

2. Feb 11, 2009

### NoMoreExams

Re: Laplace initial value problem..>.. HELP! PLEASE!

How do you have Y'(s) in there? Laplace transform takes DE and turns it into an algebraic equation. It takes PDEs and turns them into DEs.

3. Feb 11, 2009

### Kleanthis

Re: Laplace initial value problem..>.. HELP! PLEASE!

Check the given equation again to see why is that Y'(s) over there.The equation I end up is correct.

4. Feb 11, 2009

### NoMoreExams

Re: Laplace initial value problem..>.. HELP! PLEASE!

From http://en.wikipedia.org/wiki/Laplace_transform

"It is commonly used to produce an easily solvable algebraic equation from an ordinary differential equation ."

5. Feb 11, 2009

### Kleanthis

Re: Laplace initial value problem..>.. HELP! PLEASE!

The factor xy'(x) gives you Y'(s) when you apply the Laplace transform.If it s not clear enough I ll write it analytical.

6. Feb 12, 2009

### HallsofIvy

Staff Emeritus
Re: Laplace initial value problem..>.. HELP! PLEASE!

I really dislike the Laplace transform method! It only works on linear equations with constant coefficients and there are much easier ways of solving such problems.

By the way, the orginal problem was given as
y''(t)+ 4y'(t) = sin2t

y(0) = 0

Did no one point out that that is a second order equation and just saying "y(0)= 0" is not enough to specify the solutions?
That has an infinite number of solutions with different values for y' at t= 0.

7. Feb 12, 2009

### NoMoreExams

Re: Laplace initial value problem..>.. HELP! PLEASE!

You are right, let me think about it some more.