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

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

Solution:

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