Introduction to Differential Equations

We live in a world of interrelated changing entities. The position of the earth changes with time, the velocity of a falling body changes with distance, the bending of a beam changes with the weight of the load placed on it, the area of the circle changes with the size of the radius, the path of the projectile changes with the velocity and the angle at which it is fired.
In the language of mathematics, changing entities are called variables and the rate of change of one variable with respect to another a derivative. Equations which express a relationship among these variables and their derivatives are called differential equations.

Differential Equations:
An equation involving derivatives or differentials is called a differential equation.
For example,

\frac{{dy}}{{dx}}  + y = {e^x}

xdx  - ydy = 0

\frac{{{d^2}y}}{{d{x^2}}}  + y = 0

These all are called differential equations.