inverse laplace 1/(s-2)^2 — step-by-step solution

Find the causal inverse transform, for t ≥ 0. By linearity, invert each partial fraction

The inverse Laplace formula for

\frac{1}{{(s - a)}^{n}}

t^{n - 1} \cdot \frac{\exp (a t)}{(n - 1)!}

; it gives for

\frac{1}{{(s - 2)}^{2}}

\frac{t \exp (2 t)}{1!}

⇥ⓘ The factorial of a number is the product of all the integers from 1 to that number:

1!

1

⇥

\frac{t \exp (2 t)}{1}

▶Inverse Laplace transform:

t \exp (2 t)