Discussion
The solution of the first order partial differential equation \(f(x, y, z, p, q) = 0\) of the form \(F(u, v) = 0\), where u and v are functions of x, y, z is called :
Answer: B
The solution \(F(u, v) = 0\) is the general integral.
For a first order equation such as Lagrange's linear equation \(Pp + Qq = R\), if \(u = c_{1}\) and \(v = c_{2}\) are two independent integrals of the auxiliary equations, then \(F(u, v) = 0\) with F an arbitrary function is the general integral (general solution): it contains an arbitrary function, not just arbitrary constants.
A complete integral contains two arbitrary constants, \(\phi(x, y, z, a, b) = 0\). A particular integral is obtained from it by fixing the constants, and a singular integral is the envelope of the complete integral, containing no arbitrary element.
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