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## Homework Statement

Use the Laplace Transform to solve the PDE for u(x,t) with x>0 and t>0:

x(du/dx) + du/dt = xt

with IC: u(x,0) = 0 and BC: u(0,t) = 0

## Homework Equations

## The Attempt at a Solution

After taking LT of the PDE wrt t, the PDE becomes

x(dU/dx) + sU = x/(s

^{2})

Integrating factor :

I = exp([tex]\int(s/x)dx[/tex]) = x

^{s}

ODE becomes

d/dx(Ux

^{s}) = x

^{s}/s

^{2}

Integrating both sides:

U = x/(s

^{3}+s) + A(s)/x

^{s}

then I don't know how to find A(s), if I use BC, the factor 1/0 will come out...or is there some other way to calculate the PDE with LT?

thanks