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Solving differential equations

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



    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


    To solve for C i changed this to


    plugging in y=3 and x=1 i get


    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


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    Homework Helper

    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.

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


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    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

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