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!

First order linear D.E. involving i

  1. Mar 11, 2013 #1
    1. The problem statement, all variables and given/known data


    I am familiar with the standard method of obtaining a solution to a first-order, linear D.E. (i.e. using an integrating factor). However, consider the D.E. if'(x) = qf(x). It seems (after recasting the equation in the proper form) the solution suggested by the above method is f(x) = exp(iqx). However, this solution does not satisfy the original D.E. The correct solution seems to be exp(-iqx). I am curious as to why the method isn't working here. Furthermore, what general branch(s) deals with such topics if not general O.D.E.s?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 11, 2013 #2

    Curious3141

    User Avatar
    Homework Helper

    If q is a (complex) constant, and i represents the square root of -1, then this is just a simple separable ODE.

    ##if'(x) = qf(x)##

    ##\frac{f'(x)}{f(x)} = \frac{q}{i} = -iq##

    Integrating both sides wrt x,

    ##\ln(f(x)) = -iqx + \ln C##

    ##f(x) = Ce^{-iqx}##

    where C is an arbitrary (complex) constant.

    So what did you do to get the answer involving ##e^{iqx}##?
     
  4. Mar 11, 2013 #3
    Ah, I see. I was using an integrating factor:

    That is, for equations of form

    y'(x) + h(x)y(x) = g(x)

    obtaining a solution y = y(x) via y = exp(∫h(x)dx).

    But this doesn't seem to yield the same answer.
     
  5. Mar 12, 2013 #4

    Curious3141

    User Avatar
    Homework Helper

    Sure it does. Go through the working more carefully (you should show it here).

    What's the integrating factor here?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted