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

Integrating Factor ODE Fix

  1. Sep 10, 2006 #1
    Got the eqn dy/dx=x(1-y) and it can be solved both linear and separable methods.(Linear method being using a integrating factor) Problem im having is that with this two methods i get two different (yet similar answers) and was wondering if you can see my problem with this two methods im using.

    Integrating Factor method:
    y'+xy=x, u'(x)=e^(x^2/2)


    e^(x^2/2)y=integral(x*e^(x^2/2)), do u substitution, get...


    y=1+c/e^(x^2/2) or y=1+c*e^(-x^2/2)

    Separable method:
    dy/(1-y)=x dx, integrate both sides

    -ln(1-y)=e^(x^2/2)+C, raise both sides to e.

    1/(1-y)=K*e^(x^2/2)+C, rearrange to get y=.


    so we get two different answers with these methods, where is the problem lieing or are both wrong?
  2. jcsd
  3. Sep 11, 2006 #2


    User Avatar
    Science Advisor
    Homework Helper

    You got a bit sloppy near the end. Some mistakes are just typo's I think.


    So it's the same.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook