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Help with ODE

  1. May 8, 2006 #1
    Hi ,
    please can I have your help?

    x^2+2 and x^2-2 are fundamental set of solutions of a second order ODE. find the ODE.
    form:y''+p(x) y'+ q(x) y=0.

    I tried to replace the two solutions in the equation but because those solutions have exact same first and second derivatives, I found p(x)=q(x)=0 !!!!

    Can you help me to find p(x) and q(x)?
    Thank you
  2. jcsd
  3. May 9, 2006 #2


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    Homework Helper

    Try again. Write out the two equations you get and solve for p and q as if they were variables and x was a constant. The two equations will be identical except for the factor in front of q (ie, y), since the two solutions only differ in their constant term (so that all their derivatives will be equal).
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