Partial differential equations with laplas

[jd1828]

Homework Statement

Solve the partial differential equation using laplas transforms:

U`(x)=a^2*U``(t)

given U(x,0)=2


There are more initial conditions but i am just trying to get to the general solution

The Attempt at a Solution

First take laplas of the equation. Then I am trying to get it into a differential equation form that i know how to solve.

im not sure what method its called but I get

r^2 - s/(a^2)=0

Im not to sure if that is correct.

 

[jd1828]

I should add that after taking the laplas of the equation I get:

S*U(s)-2=a^2*(d^2/dx^2)U(s)

 

[stunner5000pt]

solve this using separation of variables in which you assume that u is

u(x,t) = X(x)T(t)

once you substitute this back int othe original equation you can separate that into two second order lienar DEs which you can solve easily.