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Homework Help: 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


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    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


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    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:
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