I need to solve what is underlined in red for $x_i$, nut currently I'm interested in the right side of the equation only.
On the left I sarted by doing the Laplace transform of $x_u'$ and $x_u$, and this gives the correct solution.
On the right side I tried to derive $x_u$ first, plug everything into the equation and then do the Laplace transform, and this gives a completely different solution. Is this method incorrect? Or am I doing something wrong?