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!

Need help with differential equation.

  1. May 21, 2012 #1
    Hello everyone, this is my first post in "Physics Forums"...

    I need help with this problem:

    Verify that y = (x^2/2) + ((x/2)*√(x^2 + 1)) + ln(√(x+√(x^2 +1))) is a solution of the

    equation 2y = x*y' + ln(y').....(1)

    I differentiated (y) with respect to (x), and substituted (y' and y) in equation (1), but that

    led me to nowhere.

    *The problem might be easy, but I study by myself and have no one to consult, I appreciate

    any tips or hints, thanks in advance.
     
  2. jcsd
  3. May 21, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hello Ammar Kurd! Welcome to PF! :smile:

    (try using the X2 button just above the Reply box :wink:)
    Show us what you got for y' :smile:
     
  4. May 22, 2012 #3
    Thank you for the replay, I got

    y' = x + 0.5√(x2+1) + (x2 / (2√(x2+1))) + (x+√(x2+1) / (x√(x2+1)+x2+1))

    I also tried to simplify the (y) in this way:

    y = 0.5x2 + 0.5x√(x2+1) + ln(√(x+√(x2+1)))

    = .5x(x+√(x2+1)) + 0.5ln(x+√(x2+1))

    then putting G(x) = x+√(x2+1)

    y becomes:

    y = 0.5x*G(x) + 0.5ln(G(x)), and

    y' = 0.5*G(x) +0.5xG'(x) + 0.5*(G'(x)/G(x))

    But when I substitute in the differential equation it only get complicated...

    *Thank you for the x2 tip :smile:.
     
  5. May 22, 2012 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hello Ammar Kurd! :smile:
    Yes, that's correct, except I think there should be a factor 2 in the last term. :smile:

    I don't know how you got that last term, but it simplifies, to 1/√(x2+1) :wink:
     
  6. May 22, 2012 #5
    That was my problem I didn't notice that the last term can be further simplified :redface:.

    Thank you, Problem solved :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Need help with differential equation.
Loading...