65.15.2 problem 28.2 (ii)

Internal problem ID [13834]
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 (ii)
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 )&=2 x \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=-5 x \left (t \right )-3 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.083 (sec). Leaf size: 27

dsolve([diff(x(t),t)=2*x(t),diff(y(t),t)=-5*x(t)-3*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{2 t} \\ y \left (t \right ) &= -c_{2} {\mathrm e}^{2 t}+{\mathrm e}^{-3 t} c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 36

DSolve[{D[x[t],t]==2*x[t],D[y[t],t]==-5*x[t]-3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to c_1 e^{2 t} \\ y(t)\to e^{-3 t} \left (c_1 \left (-e^{5 t}\right )+c_1+c_2\right ) \\ \end{align*}