Thread: 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


Solution:

Subsidiary equations are



The step which I do not understand is this :

Using multipliers x, y, z. we get:

each fraction=

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

Thanks for your time and effort