I have no idea where I can start to solve this problem: For the equation of minimal surfaces:$z=u(x,y)$ (i.e a surface having least area for a given contour) satisfies the second-order quasi-linear equation:
$(1+u_y^2)u_{xx} - 2u_xu_yu_{xy}+(1+u_x^2)u_{xy}=0$
a)Find all minimal surfaces of revolution about the $z$-axis (i.e $u=f(\sqrt{x^2+y^2) }$)
b) Find the differential equation for the (imaginary) characteristic curves
Seriously, I have no idea about this question then I do not know where I can start.
Any help I really appreciate. This is problem #1 -page 39 from pde 4th by Fritz John Thanks
