Re: Simple nonlinear PDE. Please help?

On Sun, 10 Jul 2005, G. A. Edgar wrote:

> In article <1120985812.003977.288080@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> Eric Gisse <jowr.pi@xxxxxxxxx> wrote:
>
> > PDE: @u^2/@x@t + u * @u/@x = exp(x)
>
> @u^2 or @^2u ?
>
> assuming the latter... the LHS is the partial derivative of something
> with respect to x, which helps
>
Well shucks, I read that as @^2 u^2 / @x@u in my previous post
@/@x (@u/@t + (1/2)u^2) = e^x
@u/@t + u^2 / 2 = e^x + g(t)

-2u'/u^2 = 1; 2/u = t + c; u = 2/(t + c)

u = 2/(t + a(x)) + (sqr 2e^x) + h(t)

where h(t) is the solution to
@h(t)/@t + h(t)^2 / 2 = g(t)







.

Quantcast