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 solution to this Differential Equation

  1. Aug 23, 2014 #1
    1. The problem statement, all variables and given/known data

    Find the solution to ## \frac{dy}{dx} = yLn(y + 1) ##

    2. Relevant equations

    ## \frac{dy}{dx} = yLn(y + 1) ##


    3. The attempt at a solution

    ## \frac{dy}{dx} = yLn(y + 1)##

    ## \frac{dy}{yLn(y + 1)} = dx ##

    but then i cant integrate, any help?
     
  2. jcsd
  3. Aug 23, 2014 #2

    Mark44

    Staff: Mentor

    Using a substitution (u = ln(y + 1)) I was able to get to this integral:
    $$\int \frac{du}{u} + \int \frac{du}{u(e^u + 1)}$$
    The first integral is very simple. The second might be amenable to another substitution, but I didn't go any further.
     
  4. Aug 23, 2014 #3
    thats what I have

    ## ∫\frac {dy}{y*ln(y+1)}=∫dx ##
    changing variables
    ## u=ln(y+1) ; du=\frac{dy}{y+1} ##

    ##\int \frac{e^u*du}{(u)*(e^u -1)} = x ##
    which is the same as

    ##\int \frac{du}{u}*\frac{e^u}{e^u-1} = x##

    and then resolving by parts dv= du/u and u=e^u/e^u-1

    ##\frac{e^u}{e^u-1}+\int \frac{ln(u)*e^udu)}{(e^u-1)^2}##

    im stuck here
     
  5. Aug 23, 2014 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I doubt there is an elementary antiderivative. Where did this problem come from?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Find the solution to this Differential Equation
Loading...