Differential Equations and The - Braun, Martin 7579 · Problem 16

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\\2 & 3 & -4\\4 & 1 & -4\end{pmatrix}\mathbf{x}+\begin{pmatrix}1\\2\\1\end{pmatrix}e^{2t}