1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Verifying if this PDE is a solution

  1. Feb 3, 2009 #1
    PROBLEM: Verify that the functions [x+1]e^(-t) ; e^(-2)sint ; and xt are respectively solutions of the nonhomogeneous equations
    Hu = -e^(-t)[x+1] ; Hu = e^(-2x)[4sint+cost] ; and Hu = x
    where H is the 1D heat operator H = [tex]\frac{\partial}{\partial t}[/tex] - [tex]\frac{\partial^2}{\partial x^2}[/tex]

    i did this the verification part,, the problem is with the second part of the problem
    Find a solution of the PDE
    Hu = [tex]\sqrt{2} x[/tex] + [Pi]e^(-2x) [4sint + cost] + e^(-t)[x+1]

    isn't the first part a solution for this PDE? i dont understand the question

    any hints how to setup this PDE?
  2. jcsd
  3. Feb 5, 2009 #2
    You have already verified some particular solutions for [tex]Hu =\phi(x,t).[/tex]
    Note that the DE is linear nonhomogeneous.

    If u1(x,t) (resp. u2(x,t)) is a solution of [tex]Hu =\phi_1(x,t)[/tex] (resp. [tex]Hu =\phi_2(x,t)[/tex] )
    u1(x,t) + u2(x,t) will be a solution of

    [tex]Hu =\phi_1(x,t) + \phi_2(x,t).[/tex]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Verifying if this PDE is a solution
  1. Solutions to this PDE? (Replies: 4)