Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solution to 2nd order diff eq

  1. Feb 22, 2007 #1
    Never mind, I figured it out.

    Here's the question:
    Find the general solution to the homogeneous differential equation

    The solution has the form https://webwork.math.uga.edu/webwork2_files/tmp/equations/06/69c97d88bd2a92e464b45652c75c181.png

    enter your answers so that https://webwork.math.uga.edu/webwork2_files/tmp/equations/b6/bf0051fdc1775f5fe9263992f485f41.png

    I'm supposed to find f1(t) and f2(t).

    I know the form ar^2+br+c=0 but in this case it's only r^2=0 so r=0.
    Also y=c1f1(t)+c2f2(t)=c1e^(r1t)+c2e^(r2t)

    f1(t)=e^(r1t) and f1(0)=1 so f1(0)=e^(r1*0)=1
    I know that's right

    I'm stuck on f2(t)
    f2(t)=e^(r2t) and f2(2)=0 so f2(2)=e^(r2*2)=2
    I tried solving for r2
    and then plugged it into e^(rt), so it was e^(.3466*t)
    This isn't right.

    I don't know what else to try. Both r1 and r2 should be equal to 0 to satisfy r^2=0, but then f2(t)=e^(rt)=e^(0*t)=1 and that wouldn't satisfy f(2)=2.

    Can anyone tell me what else I can try?

    Thanks a lot.
    Last edited by a moderator: Apr 22, 2017
  2. jcsd
  3. Feb 23, 2007 #2
    There is a problem with your attempt. You have repeated roots. The exponential form doesn't work. If that does not get you anywhere, you can just use general anti-derivatives (integrate both sides) to get the general form of the solution.

    This ought to give you the idea of the problem. I hope nobody tries to one-up my answer and gives it all away like you couldn't get it.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook