65.15.3 problem 28.2 (iii)

Internal problem ID [13835]
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)
Date solved : Tuesday, January 28, 2025 at 06:04:53 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=11 x \left (t \right )-2 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=3 x \left (t \right )+4 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.041 (sec). Leaf size: 35

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 ) &= c_{1} {\mathrm e}^{10 t}+c_{2} {\mathrm e}^{5 t} \\ y \left (t \right ) &= \frac {c_{1} {\mathrm e}^{10 t}}{2}+3 c_{2} {\mathrm e}^{5 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 95

DSolve[{D[x[t],t]==2*x[t]-2*y[t],D[y[t],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*}