Internal problem ID [11783]
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: 54
dsolve([diff(x(t),t)=-2*x(t)+3*y(t),diff(y(t),t)=-6*x(t)+4*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {{\mathrm e}^{t} \left (\sin \left (3 t \right ) c_{1} +\sin \left (3 t \right ) c_{2} -\cos \left (3 t \right ) c_{1} +\cos \left (3 t \right ) c_{2} \right )}{2} \] \[ y \left (t \right ) = {\mathrm e}^{t} \left (\sin \left (3 t \right ) c_{1} +\cos \left (3 t \right ) c_{2} \right ) \]
✓ 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*}