Differential Equations and The - Braun, Martin 7579 · Problem 12

Dynamics and Bifurcations — Braun, Martin 7579

Mathematics — Calculus · laplace-transform-systems

Problem

Find the solution of the following initial-value problem:

\dot{\mathbf{x}}=\begin{pmatrix}2 & 0 & 1\\0 & 2 & 0\\0 & 0 & 3\end{pmatrix}\mathbf{x}+\begin{pmatrix}1\\0\\1\end{pmatrix}e^{2t}, \quad \mathbf{x}(0)=\begin{pmatrix}1\\1\\1\end{pmatrix}