The above two equations can be used to solve a and b. Substituting (a,b,c) in \phi=0, we obtain the general integral. Thus a general integral describes a relation between (x,y,z,u), two known independent functions (a,b) and an arbitrary function \psi(a,b). Note that we have assumed c=\psi(a,b) to make the determinant J zero, but this is not always needed. The relations c=\psi(a) or, c=\psi(b) suffice to make the determinant zero.
