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

Solving an ODE by the method of Integrating Factors

  1. Nov 8, 2018 #1
    1. y' + y = x y2/3


    2. The problem states we need to solve this ODE by using the method of integrating factors. Every example I found on the internet involving this method was of the form:

    y' + Py = Q

    Where P and Q are functions of x only. In the problem I was given however, Q is a function of both x and y. If I try to proceed with the method I end up with:

    (d/dx) ex y = x ex y2/3


    Annnnd that's where I'm stuck. Am I missing something here or was this problem incorrectly assigned?
     
  2. jcsd
  3. Nov 8, 2018 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper

    So what do you have to do to make the right-hand side a function in ##x## only ?
     
  4. Nov 8, 2018 #3
    Divide by y2/3 on both sides of the original equation, but then I've got a term in front of the y' and that doesn't seem to get me closer to a solution.
     
  5. Nov 8, 2018 #4
    What is ##\frac{d(y^{1/3})}{dx}## equal to?
     
  6. Nov 8, 2018 #5
    Son of a...I probably would've stared at this thing for a couple of days before I noticed that. That should get me to a solution, let me give it a go.
     
  7. Nov 10, 2018 #6

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You could also proceed by noting that the righthand side is equal to ##x e^{x/3} (e^x y)^{2/3}##.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?