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How to find p and q (Charpit method) for this equation

  1. Apr 27, 2013 #1
    1. The problem statement, all variables and given/known data
    [tex] 2uq^2+y^2(q-p)=0[/tex]
    [tex]p= \partial u/\partial x [/tex]; [tex] q= \partial u/\partial y [/tex]
    find the general solution

    2. Relevant equations
    We get the charpit equations:
    [tex]\frac{dx}{-y^2}=\frac{dy}{4uq+y^2}=\frac{du}{-py^2+q(4uq+y^2)}=\frac{dp}{-2pq^2}=\frac{dq}{-2y(q-p)-2q^3}[/tex]

    I don't know how to find the value of p and q ??


    3. The attempt at a solution
    (i have tried the following ways but i cannot:
    from the original equation we have: [tex] (q-p) =-\frac{2uq^2}{y^2} [/tex]
    substitute into the last pair equation [tex]\frac{dq}{-2y(-\frac{2uq^2}{y^2})-2q^3}=\frac{dp}{-2pq^2}[/tex]
    or [tex]\frac{dq}{dp}=\frac{1}{p}(\frac{-2u}{y}+q) => q = \frac{2u}{y}+p.c1[/tex]
    but i don't know how to find p? because any pairs will lead to a complicated equation. please experts help!! thanks )
     
  2. jcsd
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