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!

Solving differential equations

  1. Feb 27, 2013 #1
    1. The problem statement, all variables and given/known data

    solve

    (y^15)x(dy/dx)=1+x

    using the initial condition y(1)=3

    express y^16 in terms of x

    2. Relevant equations



    3. The attempt at a solution

    i change the equation to the form

    y^15 dy = (1+x)/x dx
    integrating both sides i got

    y^16/16=x+lnx+C

    To solve for C i changed this to

    y=(16(x+lnx))^(1/16)+C

    plugging in y=3 and x=1 i get

    3=1.189+C

    so C=1.81079

    So my answer was y^16= 16(x+lnx)+1.81079

    this is incorrect, can anyone please explain what i may be doing wrong?
     
  2. jcsd
  3. Feb 28, 2013 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member


    Correct so far, except you shoiuld write ln(|x|).

    that is wrong. It should be y=[16(x+ln(x)+C)]1/16,
    but it has no sense. Just substitute x=1 and y=3 in the original equation
    y^16/16=x+lnx+C and isolate C.

    ehild
     
  4. Feb 28, 2013 #3
    thank you
     
  5. Feb 28, 2013 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I see know reason to solve for y (especially since you were asked to "express y^16 in terms of x"). From
    y^16/16= x+ ln|x|+ C, setting x= 1, y= 3 gives
    3^16/16= 2690420.0625= 1+ C so that C= 2690419.0625

     
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: Solving differential equations
Loading...