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: ODE with integrating factor

  1. Sep 12, 2013 #1
    Problem:
    [tex]xy'+2y=3x[/tex]
    Attempt:
    Divide by x...
    [tex]y'+\frac{2y}{x}=3[/tex]
    I think I find the integrating factor by doing:
    [tex]e^{\int \frac{2}{x}dx}[/tex]

    Not sure if that's right but if it is then the solution to the integral is just 2x.

    Any help is appreciated
     
  2. jcsd
  3. Sep 12, 2013 #2

    rock.freak667

    User Avatar
    Homework Helper

    You will need to add in the constant of integration to the right side before you do any simplification.
     
  4. Sep 12, 2013 #3

    HallsofIvy

    User Avatar
    Science Advisor

    Yes, the integrating factor is [itex]e^{\int (2/x)dx}[/itex] but then the integral is 2 ln(x) so the integrating factor is [itex]e^{2ln(x)}= e^{ln(x^2)}= x^2[/itex], not 2x.

    Multiplying the equation by that gives [itex]x^2y'+ 2xy= (x^2y)'= 3x^2[/itex]
     
    Last edited by a moderator: Sep 12, 2013
  5. Sep 13, 2013 #4
    Yeah I figured it out ends up:
    [tex]x^{2}y'+2xy=3x^{2}[/tex]
    Take integral/derivative of integrating factor:
    [tex]\int \frac{d}{dx} x^{2}y=\int 3x^{2}dx[/tex]
    Simplifies to:
    [tex]x^{2}y=x^{3}+C \implies y=\frac{x^{3}+C}{x^{2}}[/tex]
    (can be simplified a little more too)

    Thanks for the help.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Loading...