1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

How do i solve this ODE?

  1. Sep 17, 2014 #1
    1. The problem statement, all variables and given/known data
    the first one

    the second one
    2. Relevant equations

    3. The attempt at a solution
    i separated x and y variable then integrate both of them

    in the first one

    ln|y|+[itex]\frac{1}{y}[/itex]+C=- [itex]\frac{1}{x}[/itex]+ln|x|+C

    and the second one
    ∫y(y+1)dy = ∫[itex]\frac{x^{2}+1}{x}[/itex]dx


    but i can't change both of them into f(x) form or any simpler form
  2. jcsd
  3. Sep 17, 2014 #2
    It is rare that you will find a differential equation with a solution that can be written as an explicit function. Implicit solutions, the equations relating x and y that you found, are usually accepted as finding a solution to a differential equation as well. As long as there are no derivatives in your final equation, and you specify the domain of the implicit function y that is defined by your equation, where it satisfies the original differential equation, you have found a solution.
    Note, however, that you do not need two constants of integration: you may condense them into a single constant: C1 - C2 = C.
  4. Sep 18, 2014 #3
    i see, i just don't really understand the difference between implicit and explicit form, so the thing i just solve is the implicit form.. thanks for answering
  5. Sep 19, 2014 #4


    User Avatar
    Science Advisor

    The only thing to "understand" about "implicit" and "explicit" form is that the explicit form is always "y= some expression in x only" and the implicit form isn't!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted