Ordinary Differential Equations (ODEs)

Learned in MATH213. Which focuses on linear ODEs of a particular form:

Theorem 1: Linear ODEs with Variable Coefficients

All ODEs of the form $\frac{d^n}{d{t}^n}y(t)+a_{n-1}(t)\frac{d^{n-1}}{d{t}^{n-1}}y(t)+...+a_0(t)y(t)=f(t)$ where $n\in 0,1,...,n$, the $a_i(t)$ functions are real valued, but $y(t)$ and $f(t)$ can be complex valued are linear ODEs.

Here $f(t)$ is called the forcing term.

All ODEs are of the form:

$$D(y(x))=g(x)$$

where $y$ is the dependent variable, $x$ is the independent variable, $g(x)$ is the forcing term and $D$ is a differential operator.

Equations of this form appear in many ECE/CS/SE problems.