Differential equations/Introduction to First Order Linear Differential Equations

A differential equation $y'=f(t,y(t))$ is a first order differential equation. When placed in the form $y'+p(t)y=g(t)$ where $p(t)$ and $g(t)$ are functions defined on an interval $a<t<b$ is called a first order linear differential equation.

For example:

• $y'+3y=t$ where $p(t)=3$ and $g(t)=t$
• For $e^{t}y'+3y=sin(t)$ we divide through by $e^{t}$ to place the equation in the proper form and $y'+{\frac {3}{e^{t}}}y={\frac {sin(t)}{e^{t}}}$ $p(t)=3e^{-t}$ and $g(t)=sin(t)e^{-t}$

Method