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Laplace Transform of t^3 e^{4t}

Differential equations warmup

Use the table of Laplace transforms to find \(\mathcal{L}(t^{3}e^{4t})\).
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What this problem tests

Tests the ability to identify the correct formula from a Laplace transform table and substitute parameters correctly.

This is a fundamental exercise in an introductory differential equations course, introducing the use of Laplace transform tables.

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