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: First Differential Equation

  1. Apr 3, 2010 #1

    TG3

    User Avatar

    1. The problem statement, all variables and given/known data

    Find the general solution for y' +3y = t + e^(-2t) for y.

    3. The attempt at a solution

    At first I thought that since the equation was already separated, I could simply integrate both sides and get a solution easily:

    That results in 1.5 y^2 + y = .5t^2 - .5e^(-2t)
    (Unless I made a simple error, which is quite possible.)

    However, I quickly realized that this is not the approach to take, since it still contains multiple powers of y.

    So, I suspect that I will need to find an integrating factor to multiply by, (commonly called mu, I believe) but I'm not sure how you're supposed to find that.
     
  2. jcsd
  3. Apr 3, 2010 #2

    rock.freak667

    User Avatar
    Homework Helper

    For an equation

    [tex]\frac{dy}{dt}+P(t)y=Q(t)[/tex]


    an integrating factor u is given by u=e∫P(t) dt
     
  4. Apr 3, 2010 #3

    Mark44

    Staff: Mentor

    It might look separated to the most casual observer, but it's not, and further, it's not separable. You have
    dy/dt + 3y = t + e-3t

    As it sits, there's no way to get all of the terms involving y and dy on one side, and the other terms involving t and dt on the other side. An integrating factor, as rock.freak667 suggested, is the way to go.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook