1. Not finding help here? Sign up for a free 30min 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!

Stumped- DE problem

  1. Sep 27, 2005 #1
    I am stumped..... here is the problem:
    Solve the DE using the following:
    L and R are constants

    [tex]L\frac{di}{dt} + Ri = E(t)[/tex]

    [tex]i(0) = i_0[/tex]

    [tex]E(t) = E_0*sin(wt)[/tex]

    Here is my work so far:

    I got the integrating factor to become [tex]e^{Rt/L}[/tex]. But now:

    [tex]\frac{d(e^{\frac{Rt}{L}}*i)}{dt} = e^{\frac{Rt}{L}}\frac{E_0}{L}*sin(wt)[/tex]

    But I am stuck from there. Help would be appreciated.
  2. jcsd
  3. Sep 27, 2005 #2
    Since you have

    [tex]\mu(t) = e^{\frac {R}{L}t}[/tex]

    and you also have

    [tex](\mu(t)i)' = \mu(t) \frac {E_0}{L} \sin (\omega t)[/tex]

    You can integrate both sides and divide by [itex]\mu(t)[/itex]

    [tex]i(t) = \frac {\int \mu(s) \frac {E_0}{L} \sin (\omega s) ds}{\mu(t)}[/tex]

    I switched the t to a s in the numerator to avoid confusion. After you integrate the numerator, you can replace the s with a t.
  4. Sep 27, 2005 #3
    That's the problem..... I can't integrate it.
  5. Sep 27, 2005 #4

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Integrate it by parts. Let [itex]u=\sin(\omega t)[/itex] and let [itex]dv=exp\left(\frac{Rt}{L})[/itex].

    You'll have to integrate by parts twice and then algebraically solve for the integral. This integral actually pops up all the time in second order dynamic systems.
  6. Sep 27, 2005 #5


    User Avatar
    Science Advisor
    Homework Helper

    You can either integrate by parts or, if you're comfortable with complex analysis, you can note that

    [tex]\int e^{at} \sin \omega t dt = Im \int e^{(a + i \omega) t} dt[/tex]

    and extract the imaginary part after performing the integration.
  7. Sep 27, 2005 #6
    I got some really messy answer.... is that ok?
  8. Sep 27, 2005 #7

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    That depends on the answer! :biggrin:

    Why don't you post what you did so we can see it?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Stumped- DE problem