# Laplace transform

• November 7th 2010, 08:29 AM
Juggalomike
Laplace transform
How do i find the general solution of this equation using laplace transform?? its a practice problem for my exam but im not sure how to solve it.

y'''-4y'=0 when y(0)=1, y'(0)=2, y(0)''=-20
• November 7th 2010, 09:59 AM
TheEmptySet
Quote:

Originally Posted by Juggalomike
How do i find the general solution of this equation using laplace transform?? its a practice problem for my exam but im not sure how to solve it.

y'''-4y'=0 when y(0)=1, y'(0)=2, y(0)''=-20

The laplace transform of

$\frac{d^ny}{dt^n}=s^nY-\sum_{k=0}^{n-1}s^{n-k-1}y^{k}(0)$

$\mathcal{L}\{y'''\}=s^3Y-s^2y(0)-sy'(0)-y''(0)=s^3Y-s^2-2s+20$

and

$\mathcal{L}(y')=sY-1$

This gives the algebraic equation

$s^3Y-s^2-2s+20-4(sY-1)=0$

Now just solve for Y and invert the transform
• November 7th 2010, 10:16 AM
Juggalomike
ah great, thanks alot, was doing the y''' wrong.