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!

Exact solutions and the convergence of eulers method

  1. Jan 27, 2013 #1
    im having trouble with this question - http://i.imgur.com/Ars4J1b.png - more specifically with part a, as i have a good idea how to go about b. given the initial value problem

    y' = 1-t+y , y(t0)=y0

    show that the exact solution is

    y=[itex]\phi[/itex](t)=(y0-t0)et-t0+t​

    we've only spoken of approximations in class and i've just been kind of guessing as to how i should go about it so far. Ive tried to look up the term exact solutions but havent found anything of much use.


    2. Relevant equations
    integrating factor: if dy/dt+ay=g(t), then μ(t) is such that dμ(t)/dt=aμ(t). Multiply both sides of the equation dy/dt+ay=g(t) by μ(t) to obtain μ(t)dy/dt+ayμ(t)=μ(t)g(t).

    3. The attempt at a solution
    rearranging the given formula, i was able to get

    dy/dt-y=1-t​

    where a = -1. thus, dμ(t)/dt=-μ(t) making μ(t)=e-t. multiplying bothsides give

    e-tdy/dt-e-ty=e-t-te-t

    the left side can be obtained by the power-rule if the initial function was d(ye-t)/dt so we replace the leftside with this

    d(ye-t)/dt=e-t-te-t

    integrating bothsides and then solving for y gives

    y=-2-t+cet

    however, i dont think this is the correct method. What should i be doing instead of this?
     
  2. jcsd
  3. Jan 27, 2013 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Your method is fine. You just have a mistake calculating your last line. Re-check that -2-t.
     
  4. Jan 27, 2013 #3
    Thanks! Im not sure how i was integrating that wrong, but a quick check on a calculator quickly resolved the issue. I appreciate it!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Exact solutions and the convergence of eulers method
  1. Euler's Method (Replies: 6)

  2. Euler's Method (Replies: 5)

Loading...