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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


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    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


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    You could also proceed by noting that the righthand side is equal to ##x e^{x/3} (e^x y)^{2/3}##.
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