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Thread: Whoa! How did they do this ?

  1. #1
    Mar 2008

    Exclamation Whoa! How did they do this ?


    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.

    Solve the PDE
    $\displaystyle (x^2-y^2-z^2)p+2xyq=2xz$


    Subsidiary equations are

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

    The step which I do not understand is this :

    Using multipliers x, y, z. we get:

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

    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; Mar 21st 2008 at 04:04 AM.
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