Intro to Differential Equations

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.