Differential Equation

In this mathematics course, we will explore temperature, spring systems, circuits, population growth, orthogonal trajectory and biological cell motion to illustrate how differential equations can be used to model nearly everything in the world around us. We will develop the mathematical tools needed to solve differential equations. Differential equation first came into existence with the invention of calculus by Newton and Leibniz in 1671. After that Jacobi Bernoulli proposed the Bernoulli differential equation in 1695. This is an Ordinary differential equation of the form y^'+P(x)y=Q(x)y^n. Historically, the problem of vibrating string such as that of a musical instrument was studied by Jean Le Rondd’Alembert, Leonhard Euler, Daniel Bernoulli and Joseph-Louis Lagrange.