DE-BOOK Selecting Forms

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Section 10.1 Selecting Forms

Recall that the first step of the Laplace Transform Method involves a forward transformation, which converts the $y(t)$-equation into an equation containing $Y(S)$ and $s\text{.}$ Now, we skip ahead to the final step of the method, where we reverse this process to return to the $y(t)$-equation, revealing the solution to the original differential equation.

(for accessibility) — Figure 15. The Backward Laplace Transform. Converting the $Y(s)$-algebra equation back into the $y(t)$-solution.

This section will guide you through Step 3 of the Laplace Transform Method: identifying common forms, matching them to $Y(s)\text{,}$ and ultimately recovering $y(t)\text{.}$ Mastering this step will enable you to complete the solution of differential equations using the Laplace Transform Method.

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