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!

Find the particular solution of the differential equation

  1. Mar 24, 2010 #1
    Find the particular solution of the differential equation

    dy/dx = (3x+42y)/7x

    satisfying the initial condition y(1) = 5.

    Attempt:
    dy/dx = 3/7 + 6y/x

    dy/dx - 6y/x = 3/7

    p(x) = -6/x
    q(x) = 3/7

    u(x) = -6 ∫(1/x)dx = -6ln|x|
    e^(u(x)) = -x^6


    1/e^(u(x)) ∫e^(u(x))q(x)dx

    = 1/(-x^6) ∫(-x^6)(3/7)dx

    = 3/(7(-x^6)) [(-x^7/7)+c]

    =3x/49 - 3c/(7x^6)


    y(1) = 5 = 3(1)/49 - 3c/(7(1)^6)

    5 = 3/49 - 3c/7

    242/49 = -3c/7

    c = -242/21


    So, what I got is

    y(x) = 3x/49 + 242/(49x^6)

    however, my professor said it's wrong. So, can anybody tell me what I did wrong? I'll be very appreciated. thanks.
     
  2. jcsd
  3. Mar 24, 2010 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member


    [tex]e^u=e^{-6\ln|x|}=\left(e^{\ln|x|}\right)^{-6}=|x|^{-6}=x^{-6}\neq -x^6[/tex]

    :wink:

    It's always a good idea to check your answers before submitting them. Does this solution satisfy your original ODE?
     
  4. Mar 24, 2010 #3
    Just to be sure, the answer is

    [tex]y(x) = -3x/35 + 178/(35x^{6})[/tex]

    right?
     
    Last edited: Mar 24, 2010
  5. Mar 24, 2010 #4

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    You mean [tex]y(x) = -\frac{3}{35}x + \frac{178}{35}x^6[/tex]...right? If so, then yes.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook