Question

A friend is using Laplace Transforms to solve a differential equation. On one line of his work you see 1/(s-2)+e⁻³ᵗ. Explain why you are sure your friend has made a mistake, given what we know about s and t.

Answer 1

The Laplace Transform expression 1/(s-2)+e⁻³ᵗ is incorrect. The correct expression is e^(2t) + e⁻³ᵗ.

Step-by-step explanation:

The expression 1/(s-2)+e⁻³ᵗ that your friend is using is incorrect. From what we know about s and t, we can see that the Laplace Transform expression should be
e^(2t) + e⁻³ᵗ.

The Laplace Transform is used to solve differential equations and represents a transformation from the time domain (t) to the frequency domain (s). In this case, the correct Laplace Transform should include terms involving e^(at) where 'a' represents a coefficient like 2 or -3.

Therefore, your friend made a mistake by using 1/(s-2)+e⁻³ᵗ instead of
e^(2t) + e⁻³ᵗ.