1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Use an integrating factor to solve

  1. Feb 23, 2014 #1
    1. The problem statement, all variables and given/known data

    Use an integrating factor to determine the general solutions of the following differential
    equation:

    dx/dt - 2/t = 2t3 + (4t2)(e4t)


    2. Relevant equations

    R(x) = e∫P(x).dx

    3. The attempt at a solution

    Usually the equation is in the form dx/dt + P(x)t = Q(x) but here I'm not sure what to do to find P(x) here as I have 1/t, t3 and t2.

    I'm also not sure how to go about finding a solution either. I know that once I have found the integrating factor, I have to multiply the original equation by R(x). After that I'm not sure what to do.
     
  2. jcsd
  3. Feb 23, 2014 #2
    Well, it looks like this equation is actually separable. Just move the -2/t over, and the right side will be entirely a function of t.
     
  4. Feb 23, 2014 #3
    I realised that whilst I was doing it, but the question specifically asks me to use an integrating factor. thanks for the reply though.
     
  5. Feb 23, 2014 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Here, your independent variable is ##t##. So your integrating factor is ##R=e^{\int\frac 2 t~dt}##. Evaluate that and multiply through by it.
     
  6. Feb 23, 2014 #5
    Oh, I see. Thanks, I was being a bit stupid there.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted