How to solve a partial differential equation with 3 variables?

Question

I have just learned the Characteristic Method with 2 variables to solve Partial diferential équations... I would like to know how to solve the next partial diferential equation with 3 variables

$$ \frac{df}{dx}+ Q(z_1)\frac{df}{dz_2}+ Q(z_2)\frac{df}{d z_2}=P(x,z_1,z_2)f $$ I know that the first thing to do is to write the Lagrange-Charpit équations

Is it something similar to the Lagrange Charpit equation with 2 variables?

Thank you for any advice

Answer 1

$$ \frac{df}{dx}+ Q(z_1)\frac{df}{dz_1}+ Q(z_2)\frac{df}{d z_2}=P(x,z_1,z_2)f $$ $$ \frac{dx}{1}= \frac{dz_1}{Q(z_1)}= \frac{dz_2}{Q(z_2)}=\frac{df}{P(x,z_1,z_2)f} $$