ABSTRACT
The origin of differential equations naturally arises from the study of calculus, discovered independently by British physicist and mathematician Newton and German mathematician and diplomat Leibniz. Daniel Bernoulli, son of Johann Bernoulli, derived partial differential equations for fluid mechanics, whereas Leonhard Euler, a student of Johann Bernoulli, derived and applied differential equations for mechanics analysis. The method of integrating factors for ordinary differential equations (ODE) was discovered by Euler, and he was responsible for the first systematic solution technique for solving differential equations. Lagrange, an Italian-born French mathematician, contributed significantly to the development of theory for the solutions of differential equations, particular for the particular solution for nonhomogeneous ODEs and first order partial differential equations (PDE). One major problem in solving nonlinear PDEs or ODEs is that nonlinear differential equations may have more than one solution at some points of the independent variables.
