Internal problem ID [12109]
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).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=13 x \left (t \right )\\ y^{\prime }\left (t \right )&=13 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
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 ) &= {\mathrm e}^{13 t} c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.065 (sec). Leaf size: 65
DSolve[{x'[t]==13*x[t],y'[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*}