i have stalled in another problem.

Given that when

Solving using partial fractions:

Therefore:

is the solution. however if i take the inverse of that does not match the solution.

can you spot where i have gone wrong ?

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I seem to be making the same mistake again with this question:

Given that:

and when

Taking Laplace Transforms:

Now solving using partial fractions:

From which:

and

Hence:

The solution gives

What step am i missing out or where have i gone wrong ?