Question

Use appropriate algebra and Theorem 7.2 .1 to find the given inverse Laplace transform. (Write your answer as a function of t .) L⁻¹((1/s²)-(1/s)+1(/s-3))

Answer 1

The inverse Laplace transform of the given expression (1/s²) - (1/s) + (1/(s-3)) is t - 1 + e³⁴t.

Step-by-step explanation:

The question asks for the inverse Laplace transform of the algebraic expression (1/s²) - (1/s) + (1/(s-3)). According to the properties of the Laplace transform, the inverse transform of 1/s² is t, the inverse of 1/s is the constant function 1, and the inverse of 1/(s-3) is e³⁴t. Therefore, the inverse Laplace transform of the given expression is t - 1 + e³⁴t.