Answer to Question #157202 in Differential Equations for Tha

Question

Solve for complete integral

z=px+qy+c√(1+p²+q²)

Answer 1

This PDE is of Clariut's type. That is, it's of the form $z=px+qy+f(p, q)$.

To get the complete integral of this kind of PDE, we replace $p, q$ with $a, b$ respectively.

Hence the complete integral of the PDE above is

$z=ax+by+c\sqrt{(1+a^2+b^2)}$