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Diff. eq. solve linear equation

  1. Mar 1, 2014 #1
    1. The problem statement, all variables and given/known data

    Solve the following differential equations.

    3xy'+y=12

    2. Relevant equations

    I believe this is a linear equation problem. So I believed to have solved it, however I am not sure if I have done so correctly.

    3. The attempt at a solution
    20140301_115639_zps4db21c0a.jpg
     
  2. jcsd
  3. Mar 1, 2014 #2
    If you're not sure, take the derivative and you can verify it from the equation given. The only mistake I see is in calculating your integrating factor:

    When you have [itex]e^{\frac{1}{3}lnx}[/itex], you have to move the 1/3 into the exponent on the [itex]lnx[/itex] before you cancel the e and the ln.
     
  4. Mar 1, 2014 #3
    thank you for the advice.
    I see what you mean. so when the e and the ln cancel out, i should be left over with x^(1/3) as my integrating factor correct?
     
  5. Mar 1, 2014 #4
    Yes, that looks right. That should give you the right answer.
     
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