Solve linear system of ODEs using Laplace transform

Question

I need to solve the following initial value problem via Laplace transform \begin{align*} \dot{\mathbf{x}} = \begin{pmatrix} 2 & -5 \\ 1 & -2 \end{pmatrix} \mathbf{x} + \begin{pmatrix} \sin t \\ \tan t \end{pmatrix} , \: \mathbf{x}(0) = \begin{pmatrix} -1 \\ 0 \end{pmatrix} \end{align*} but I don't know how to do that since there's no Laplace transform for the tangent function.

Answer 1

There is Laplace transform for tangent function, but it's complicated and using digamma function. Laplace transform