Voltera Integral Equation

Equation of the form

\begin{aligned} f (t) & = g (t) + (f * h) (t), t \geq 0 \\ = g (t) + \int_{0}^{t} f (t - τ) h (τ) d τ \end{aligned}

Where $g (t)$ and $h (t)$ are given function.

Use the Laplace Transform with Convolution to solve it

Steps

Take Laplace of both sides
Calculate specific Laplace of $f ()$ and $h ()$
Reduce down to functions of $F (s) = L (t)$
Isolate for $F (s)$
Perform Partial Fraction Decomposition
Take Inverse Laplace Transform