How to Solve Inverse Laplace Transform: Factor or Use Complex Methods?

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SUMMARY

The discussion centers on the methods for solving the inverse Laplace transform of the function involving the polynomial (s^2 + 5s + 6). The participant initially factored the polynomial as (s + 3)(s + 2) but opted for a more complex method, resulting in incorrect coefficients A = -1, B = -1, and C = 1. The simpler factoring approach yields a straightforward exponential solution, while the complex method led to a loss of points on the exam. The consensus suggests that while both methods are valid, the simpler approach is preferred for accuracy and efficiency.

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I have to take the inverse laplace transform of the above function. Now, I know that I can factor (s^2+5s+6) as (s+3)(s+2) and take the easy way out. However, I did it as above on a test, getting A = -1, B = -1, and C = 1. I then took the inverse laplace transform and got something involving cosh's and sinh's. Doing it the easy way would have gotten you just the exponential e. This problem on the exam was maybe 30+ points and I got 0 points for this problem because I did not realize to factor (s^2+5s+6) and did it the way more complicated way. Is my method justified and most importantly, right?
 
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Your method looks alright (so far), but you don't get the values you stated for A, B & C. Zero marks out of 30 seems a bit harsh though, as you at least demonstrated that you know partial fraction decomposition can be used for this. I'd talk to your professor to see if you can't get some partial credit for that at least.
 

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