Internal problem ID [12099]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 28, Distinct real eigenvalues. Exercises page 282
Problem number: 28.2 (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 )&=3 x \left (t \right )+4 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
dsolve([diff(x(t),t)=11*x(t)-2*y(t),diff(y(t),t)=3*x(t)+4*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{5 t} c_{1} +c_{2} {\mathrm e}^{10 t} \\ y \left (t \right ) &= 3 \,{\mathrm e}^{5 t} c_{1} +\frac {c_{2} {\mathrm e}^{10 t}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 95
DSolve[{x'[t]==2*x[t]-2*y[t],y'[t]==3*x[t]+4*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{5} e^{3 t} \left (5 c_1 \cos \left (\sqrt {5} t\right )-\sqrt {5} (c_1+2 c_2) \sin \left (\sqrt {5} t\right )\right ) \\ y(t)\to \frac {1}{5} e^{3 t} \left (5 c_2 \cos \left (\sqrt {5} t\right )+\sqrt {5} (3 c_1+c_2) \sin \left (\sqrt {5} t\right )\right ) \\ \end{align*}