Internal problem ID [12103]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 29, Complex eigenvalues. Exercises page 292
Problem number: 29.3 (ii).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-2 x \left (t \right )+3 y \left (t \right )\\ y^{\prime }\left (t \right )&=-6 x \left (t \right )+4 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 53
dsolve([diff(x(t),t)=-2*x(t)+3*y(t),diff(y(t),t)=-6*x(t)+4*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{t} \left (c_{1} \sin \left (3 t \right )+c_{2} \cos \left (3 t \right )\right ) \\ y \left (t \right ) &= {\mathrm e}^{t} \left (c_{1} \cos \left (3 t \right )+c_{2} \cos \left (3 t \right )+c_{1} \sin \left (3 t \right )-c_{2} \sin \left (3 t \right )\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 56
DSolve[{x'[t]==-2*x[t]+3*y[t],y'[t]==-6*x[t]+4*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^t (c_1 \cos (3 t)+(c_2-c_1) \sin (3 t)) \\ y(t)\to e^t (c_2 \cos (3 t)+(c_2-2 c_1) \sin (3 t)) \\ \end{align*}