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Differential equation dx/x(z-2y^2) = dy/y(z-y^2-2x^3) = dz/z(z-y^2-2x^3)

  1. Jan 29, 2012 #1
    1. The problem statement, all variables and given/known data

    Solve
    dx/x(z-2y^2) = dy/y(z-y^2-2x^3) = dz/z(z-y^2-2x^3)



    2. Relevant equations



    3. The attempt at a solution
    i got one solution by taking

    dy/y(z-y^2-2x^3) = dz/z(z-y^2-2x^3)

    dy/y= dz/z
    integ: to bothsides

    ln y = ln z + ln c
    ln y = ln (zc)
    y=zc

    y/z= c

    now i am looking for next solution kindly help.
     
  2. jcsd
  3. Jan 29, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Now, you can replace y by cz in
    [tex]\frac{dx}{x(z-2y^2)}= \frac{dz}{z(z- y^2- 2x^3)}[/tex]
     
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