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Math Help - Whoa! How did they do this ?

  1. #1
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    Mar 2008
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    Exclamation Whoa! How did they do this ?

    Hi,

    I am trying to learn partial diff equations myself and I'm stuck with this small step which I do not understand. I hope someone will help me.

    Question:
    Solve the PDE
    (x^2-y^2-z^2)p+2xyq=2xz

    Solution:

    Subsidiary equations are

     \frac{dx}{x^2-y^2-z^2}=\frac{dy}{2xy}=\frac{dz}{2xz}

    The step which I do not understand is this :

    Using multipliers x, y, z. we get:

    each fraction= \frac{xdx+ydy+zdz}{x(x^2+y^2+z^2)}

    Rest of the solution I understand but I don't get that how they did this particular step.

    Thanks for your time and effort
    Last edited by Abhishek; March 21st 2008 at 04:04 AM.
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