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General Solution to Differential Equation?

  1. Oct 18, 2011 #1
    Problem Statement

    Find the general solution to ty'-4y=(t^6)*(e^t)

    Solution Attempt

    I added the 4y over and divided by t

    y'=[(t^6)(e^t)+4y] / t

    I am not sure where to go from here. I'm pretty sure that separation of variables wont work, because I don't think that I can separate the 4y from t.

    Now I think I should have just divided through by t and then used integrating factors with [itex]\mu[/itex]=e^(-4ln|t|)=t^-4

    Is this correct? Thanks for your help!

    EDIT: I've found the solution... It did seem like using integrating factors worked the best. The answer is

    y = [(te^t)-(e^t)+c] / (t^-4)
     
    Last edited: Oct 18, 2011
  2. jcsd
  3. Oct 18, 2011 #2

    Dick

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    I think using that integrating factor is a great idea. Can you finish from there?
     
  4. Oct 18, 2011 #3
    Yup already finished. The problem got much simpler as things began to cancel. I love it when problems work out nicely. Thanks (:

    I think the main thing that hung me up was changing gears from studying how to solve differential equations using Laplace Transforms back to using integrating factors.
     
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