Vault Of Euclid

Inverse Laplace Transform with a Time Delay

Differential equations warmup

Use (8.4.12) to find \[ \mathcal{L}^{-1}\left(\frac{e^{-2s}}{s^2}\right). \]

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What you need first

Basic Laplace transforms
The Heaviside step function

What this problem tests

Tests the ability to recognize and apply the Second Shifting Theorem for inverse Laplace transforms.

This problem typically appears in a differential equations course when learning to solve linear ODEs with discontinuous forcing functions.

More on Differential equations

Inverse Laplace Transform of a Rational Function Sum warmup

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