65.17.4 problem 30.1 (iv)

Internal problem ID [13845]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 30, A repeated real eigenvalue. Exercises page 299
Problem number : 30.1 (iv)
Date solved : Tuesday, January 28, 2025 at 06:05:01 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=13 x \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=13 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 19

dsolve([diff(x(t),t)=13*x(t),diff(y(t),t)=13*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{13 t} \\ y \left (t \right ) &= c_{1} {\mathrm e}^{13 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 65

DSolve[{D[x[t],t]==13*x[t],D[y[t],t]==13*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to c_1 e^{13 t} \\ y(t)\to c_2 e^{13 t} \\ x(t)\to c_1 e^{13 t} \\ y(t)\to 0 \\ x(t)\to 0 \\ y(t)\to c_2 e^{13 t} \\ x(t)\to 0 \\ y(t)\to 0 \\ \end{align*}