An analytical solution of Monge differential equation

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.