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Solving this PDE

  1. Dec 22, 2006 #1
    Solving this PDE :(

    Hello i have a question about this..let be a function [tex] F(x(t),y(t),z(t),t) [/tex] then if we use the "total derivative" respect to t and partial derivatives..could we find an F so it satisfies:

    [tex] \frac{d (\frac{\partial F}{\partial x})}{dt}+\lambda F + (\frac{\partial F}{\partial y})^{2}=0 [/tex] ??

    how could you solve that ??.. my big problem is that this involves "total" and partial derivatives respect to x and y all mixed up.:yuck: :yuck:
  2. jcsd
  3. Jan 4, 2007 #2

    Since the equation includes total derivative with respect to t, then x, y and z are functions of t as already included in the argument of F; X(t) .................

    However, you still can solve it, but in terms of dx/dt, dy/dt, dz/dt .......... etc. But, here, only function in dx/dt, dy/dt and dz/dt.

    Try this:
    where p/px is the partial derivative.
    This can be done by the rule of differentials.
    Here, T(r>,t)=pF/px

    You will get a normal partial differential function in x, y and z with 3 time-dependent functions (considered to be constants in the equation). Solve it, if this form has an analytical solution (or any other sort) in PDEs.

    Engineer\ Amr Morsi.
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