Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Doubts about change of variable in ODE

  1. Jul 13, 2008 #1
    I was trying to check some calculations from a paper myself and I got
    stuck at a differential equation. Can anybody help me with suggestions?
    I am giving a simpler version of the differential eqn by setting all numerical
    constants=1. Consider:
    We change variable to
    then the ODE is
    The author writes the solution is:
    z(y)=\frac{1}{u^{3/2}}z(u)=u\left(J_{\frac{1}{2}}(u)+c_1N_{\frac{1}{2}}(u) \right)
    where J and N are Bessel functions. My problem is, I am getting the relation
    z(u)=u\left(c_1 J_{\frac{1}{2}}(u)+c_2 N_{\frac{1}{2}}(u) \right)
    But note that according to the author,
    z(y)={u^{5/2}}\left(J_{\frac{1}{2}}(u)+c_1N_{\frac{1}{2}}(u) \right)
    Or in other words though I can get the desired solution in terms of changed variable,
    I am not able to get the relation:
    at all. How to get this relation? Also, note that the author uses one constant
    in the solution but I think there should be two independent constants. What am I missing in the calculations?
    Last edited: Jul 13, 2008
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Discussions: Doubts about change of variable in ODE
  1. Change of Variables (Replies: 10)