Recent content by javicg

I have been working on it and this is what I have now. We take the Laplace transform in the t variable. \mathcal{L}\left(2x \frac{\partial u}{\partial t} \right) = 2x \int_0^{\infty} \frac{\partial u}{\partial t} e^{-st} dt = 2x (-u(x,0) + \bar{U}(x,s)), where \bar{U}(x,s)...

I had it proposed by my uncle, who is a teacher btw. It could be easily from a textbook, but I don't know which one. Also, my first post was actually on Sep6-09.

I'm having trouble with the following related questions. Any help is appreciated. (a) Show that a change of variables of the form \xi = px + qt, \eta = rx + st can be used to reduce the one dimensional wave equation \frac1{c^2} u_{tt} = u_{xx} to an equation of the form \frac{\partial^2...

I have exactly the same problem. These are all the conditions: By using the Laplace transform, obtain as an integral the solution of the first order PDE x^2 \frac{\partial u}{\partial x} + 2x \frac{\partial u}{\partial t} = g(t), subject to u(x, 0) = 0, u(1, t) = 0. The function g is...

I have to solve the nonlinear DE y'=x²-y² by using an infinite series expansion y=\sum_{n=0}^{\infty} a_n x^n, but I've tried in vain. Maybe a change of variables would make it easier, but I don't know which one. Thanks