Internal problem ID [11787]
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 (ii).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-6 x \left (t \right )+2 y \left (t \right )\\ y^{\prime }\left (t \right )&=-2 x \left (t \right )-2 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve([diff(x(t),t)=-6*x(t)+2*y(t),diff(y(t),t)=-2*x(t)-2*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {{\mathrm e}^{-4 t} \left (2 c_{2} t +2 c_{1} -c_{2} \right )}{2} \] \[ y \left (t \right ) = {\mathrm e}^{-4 t} \left (c_{2} t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 46
DSolve[{x'[t]==-6*x[t]+2*y[t],y'[t]==-2*x[t]-2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-4 t} (-2 c_1 t+2 c_2 t+c_1) y(t)\to e^{-4 t} (-2 c_1 t+2 c_2 t+c_2) \end{align*}