# Laplace Transform

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?

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.

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

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

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

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

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.

HallsofIvy
Homework Helper

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.

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.

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