First-Order Linear Differential Equations

Abstract

Consider the first-order linear differential equation $y'+p(t)y~=~q(t),~~~'=\frac{d~}{dt}$ where the functions p and q are continuous in an open interval $I=(\alpha ,\beta )$ [1]. We can find the general solution of (1.1) in terms of the known functions p and q by multiplying both sides of (1.1) by an integrating factor $e^{P(t)}$, where P(t) is a function such that $P'(t)=p(t)$.