ABSTRACT
Nearly all textbooks on partial differential equations (PDEs) will cover second order PDEs, like the wave equation, diffusion equation, and potential or Laplace equation. However, the discussion of first order PDEs is normally not covered in elementary textbooks on PDE. The method of solution is quite different from that for second order and the general solution for first order PDEs will include an arbitrary function of some characteristics line. The first order PDE before discussing the second order PDE, historically the second order PDE was investigated before the first order. Bernoulli, Euler, D’Alembert and others considered the physical problem related to dynamics of rigid bodies, vibrations of membranes, and wave phenomena. These are second order PDE. The solution of first order PDEs was considered mainly by Lagrange, Clairaut, D’Alembert, Monge, ChaIpit, Jacobi, and others.
