Differential Equations and The - Braun, Martin 7579 · Problem 17

Dynamics and Bifurcations — Braun, Martin 7579

Mathematics — Calculus · particular-solution-matrix-ode

Problem

Find a particular solution

\psi(t)

of the given differential equation of the form

\psi(t)=e^{\lambda t}(\mathbf{a}+\mathbf{b}t)

\dot{\mathbf{x}}=\begin{pmatrix}1 & -1 & -1\\1 & 3 & 1\\-3 & 1 & -1\end{pmatrix}\mathbf{x}+\begin{pmatrix}1\\-1\\-1\end{pmatrix}e^{3t}