Internal problem ID [11784]
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 (iii).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-11 x \left (t \right )-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=13 x \left (t \right )-9 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 59
dsolve([diff(x(t),t)=-11*x(t)-2*y(t),diff(y(t),t)=13*x(t)-9*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -\frac {{\mathrm e}^{-10 t} \left (\sin \left (5 t \right ) c_{1} +5 \sin \left (5 t \right ) c_{2} -5 \cos \left (5 t \right ) c_{1} +\cos \left (5 t \right ) c_{2} \right )}{13} \] \[ y \left (t \right ) = {\mathrm e}^{-10 t} \left (\sin \left (5 t \right ) c_{1} +\cos \left (5 t \right ) c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 69
DSolve[{x'[t]==-11*x[t]-2*y[t],y'[t]==13*x[t]-9*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{5} e^{-10 t} (5 c_1 \cos (5 t)-(c_1+2 c_2) \sin (5 t)) y(t)\to \frac {1}{5} e^{-10 t} (5 c_2 \cos (5 t)+(13 c_1+c_2) \sin (5 t)) \end{align*}