(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Whoa! How did they do this ?

Hi,

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

The problem statement, all variables and given/known data

Solve the Partial Differential Equation

[tex](x^2-y^2-z^2)p+2xyq=2xz[/tex]

Solution given in the book

Subsidiary equations are

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

The step which I do not understand is this :

Using multipliers x, y, z. we get:

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

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

Thanks for your time and effort

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# Homework Help: Whoa! How did they do this ?

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