  We present the exact solution to the non linear Monge differential equation
lambda(x, t)lambdax(x, t) = lambdat(x, t). It is widely accepted that the Monge
equation is equivalent to the ODE d2X/dt2= 0 of free motion for particular
conditions. Furthermore, the Monge Type equations are connected with X =
F(dX/dt, X; t), which can be integrated with quadratures [1]. Other asymptotic
solutions are discussed, see e.g. [2]. The solution was reached with
calculations that depend upon dimensional representation, which is given by (x,
t) coordinates. We present this analytical solution to the Monge differential
equation as an implicit solution.
