This is the first in a series of posts I plan on writing about Engineering Mathematics. It assumes prior knowledge of Calculus.

An equation that contains derivatives of one or more functions is called a differential equation. Consider the equation

y=e^x

The derivative of y with respect to x is:

y'=e^x

Therefore, combining the equations above, we can say that:

y'=y

This is called a differential equation. Now let’s modify our equation:

y=e^{2x}

The derivative becomes: y'=2e^{2x}, so combining both equations, we can say that:

y'=2y

We can further modify our equation: y=e^{2x^2} so the derivative becomes: y'=4xe^{2x^2}. We can say that:

y'=4xy

Over the next few lessons we will learn about how to identify and solve differential equations.