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!

Integration by parts of 4th order DE

  1. Oct 24, 2008 #1
    having difficulty integrating the following equation by parts to determine if its symmetric:

    d4 u / dx4 + K d2 u / dx2 + 6 = 0 0< x < 1

    Can someone help with this?
  2. jcsd
  3. Oct 24, 2008 #2


    User Avatar
    Homework Helper

    If K is a constant then you have a 4th order DE with constant coefficients. So that all of your answers will be in the form y=erx.

    d4u/dx4 + K d2u/dx2 + 6=0
  4. Oct 24, 2008 #3
    But I'm lost with assigning u, v, du, dv to this equation? Also can I split it into three idfferent integrals added together or must I assign the values and differentiate the hole equation by parts? Not for sure if I'm being clear?
  5. Oct 24, 2008 #4


    User Avatar
    Homework Helper

    [tex]\frac{d^4u}{dx^4} + K \frac{d^2u}{dx^2} + 6=0[/tex]

    Now you can just integrate everything with respect to x to get

    [tex]\int \frac{d^4u}{dx^4}dx + \int K \frac{d^2u}{dx^2}dx + \int 6dx= \int 0dx[/tex]

    Now [itex]\int \frac{dy}{dx}dx=y+c[/itex] where c is a constant. Now just use this idea to work out your problem.
  6. Oct 25, 2008 #5


    User Avatar
    Staff Emeritus
    Science Advisor

    This is NOT a first order equation: you can't just integrate both sides. rockfreak667 told you to do it as an equation with constant coefficients. What is its characteristic equation?

    And what is [itex]\int d^2y/dx^2 dx[/itex]?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Integration by parts of 4th order DE