Question

find the Bounded solution for the following Parabolic differential equation using Laplace Transform.

Answer 1

Damn PDE .. my next topic

Answer 2

\[sU-f(x)=c^2U_{xx}\]\[sU-c^2U_{xx}=f(x)\]?

Answer 3

yes.

Answer 4

im still unsure about prev...did u solved it?

Answer 5

because we have a similar problem here

Answer 6

there is something crazy with Particular solution part !

Answer 7

man this is really crazy

Answer 8

\[\Large U_{xx}-\frac{s}{c^2}U=-\frac{f(x)}{c^2}\]
the complementary Part is
\[\Large U(x,s)=Ae^{\frac{\sqrt{s}}{c}}+Be^{-\frac{\sqrt{s}}{c}}\]

Answer 9

yup it is .

Answer 10

@amistre64

Answer 11

i believe that we must use variation of parameters for particular solution

Answer 12

@hartnn any idea.

Answer 13

thread is dead ... i thought i would get some practice.