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Integration within a DiffEQ problem

  1. Sep 22, 2008 #1
    1. The problem statement, all variables and given/known data
    Solve the given differential equation by using an appropriate substitution.



    2. Relevant equations
    [tex](x^{2}+xy+3y^{2})dx-(x^{2}+2xy)dy=0[/tex]
    [tex]y=ux, dy=udx+xdu[/tex]


    3. The attempt at a solution
    [tex](x^{2}dx+ux^{2}dx+3u^{2}x^{2}dx)-(ux^{2}dx+x^{3}du+2u^{2}x^{2}dx+2ux^{3}du)=0[/tex]
    After combining, cancelling and moving terms into their appropriate places, I get:
    [tex]\frac{dx}{x}=\frac{2u+1}{u^{2}+1}du[/tex]


    This is where I get stuck, I am unable to integrate the right hand side. Can anyone help me out a little?

    Thanks.
     
  2. jcsd
  3. Sep 22, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Split it into two parts. 2u/(u^2+1) looks easy by a substitution and 1/(u^2+1) looks like an arctan.
     
  4. Sep 22, 2008 #3
    I cannot believe I didn't see that.

    Thanks!!!
     
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