Internal problem ID [11788]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 30, A repeated real eigenvalue. Exercises page 299
Problem number: 30.1 (iii).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-3 x \left (t \right )-y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )-5 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve([diff(x(t),t)=-3*x(t)-y(t),diff(y(t),t)=x(t)-5*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{-4 t} \left (c_{2} t +c_{1} +c_{2} \right ) \] \[ y \left (t \right ) = {\mathrm e}^{-4 t} \left (c_{2} t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 44
DSolve[{x'[t]==-3*x[t]-y[t],y'[t]==x[t]-5*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-4 t} (c_1 (t+1)-c_2 t) y(t)\to e^{-4 t} ((c_1-c_2) t+c_2) \end{align*}