Section 2.2
More on F.O.L.'s

Existence and Uniqueness Theorem for F.O.L.'s

Theorem: If the functions p and g are continuous on an open interval $I:\alpha < t < \beta$ containing the point t = t₀, then there exists a unique function $y=\phi(t)$ that satisfies the differential equation

y' + p(t) y = g(t)

for each t in I, and that also satisfies the initial condition y(t₀) = y₀, where y₀ is an arbitrary prescribed initial value.