While studying about PDEs I found that we can calculate the general solution of a PDE from it's complete solution.
The method goes like this:
If say, a PDE $F(x,y,z,p,q)=0$ where $p=z_x,q=z_y$ is given, and $f(x,y,z,a,b)=0$ is a complete solution of $F,$ then assume $b$ to be an unknown function of $a$ say, $b=\phi(a).$
So, the complete solution $f$ becomes, $f(x,y,z,a,\phi(a))=0.... (1)$
Now, differentiating the above equation wrt $a$ we get, $f_a(x,y,z,a,\phi(a))+f_b(x,y,z,a,\phi(a))\phi'(a)=0.... (2)$