The forum discussion centers on solving the inverse Laplace transformation of the function $$\mathscr{L}_s^{-1} \left\{ \frac{s}{s^2-s+\frac{17}{4}} \right\}$$. The correct solution is identified as $$f(t) = (1/4)e^{t/2}(\sin(2t) + 4\cos(2t))$$. Participants emphasize the importance of breaking down the function into more recognizable Laplace transforms and suggest completing the square in the denominator as a starting point for the solution.
PREREQUISITESStudents studying differential equations, mathematicians focusing on transform methods, and educators teaching Laplace transform techniques.
END said:Homework Statement
Solve the following:
$$\mathscr{L}_s^{-1} \left\{ \frac{s}{s^2-s+\frac{17}{4}} \right\}$$
Homework Equations
Table of Laplace Transforms.The Attempt at a Solution
The solution is
$$f(t) = (1/4 )e^{t/2} (\sin(2 t)+4 \cos(2 t))$$
I know I need to break up ##F(s)## into more common Laplace transforms, but I'm not quite sure how to begin.