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!

Homework Help: Solving a First Order Initial Value Problem

  1. Nov 2, 2014 #1
    1. The problem statement, all variables and given/known data
    If y = y(t) is the solution of the initial value problem
    y' + (2 t + 1) y = 2 cos(t)
    y(0) = 2
    What is y''(0)?

    2. Relevant equations

    3. The attempt at a solution
    Since this is a first order linear, I started out by finding the integrating factor so I can find what y is, and then just take the second derivative of it, and then put it to 0.

    [itex] IF = e^{ \int {2t + 1} } => IF = e^{t^2 + t} [/itex]
    Then, I end up with this equation, if we set IF = k.
    [itex] (ky)' = k (2 cos(t)) [/itex]

    From here, I don't think I can integrate that equation, so now I'm pretty much stuck. Is there a method I'm missing? Or could I find the value of the second derivative using the value of y at 0?
    Any help is appreciated, thank you.
  2. jcsd
  3. Nov 2, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Instead of trying to solve the original DE, try just differentiating it once and solving for ##y''## and see if you can get the answer from that.
  4. Nov 2, 2014 #3
    Wow! I can't believe I didn't see that, haha, thanks man. Much appreciated.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted