Find the integral surface of x(y^2+z)p-y( x^2+z)q=(x^2-y^2)z through the straight through the x+y = 0,z = 1.
Lagrange’s auxiliary equations of are
thus, the solution is the system of equations:
Taking as a parameter, the given equation of the dtraight line can be put in parametric form .
may be re-written as
Eliminating from the equations , we have
Putting values of and, the desired integral surface is