Internal problem ID [12566]
Book: Nonlinear Ordinary Differential Equations by D.W.Jordna and P.Smith. 4th edition 1999.
Oxford Univ. Press. NY
Section: Chapter 2. Plane autonomous systems and linearization. Problems page 79
Problem number: 2.2 (vi).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )\\ y^{\prime }\left (t \right )&=y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve([diff(x(t),t)=x(t),diff(y(t),t)=y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{t} \\ y \left (t \right ) &= c_{1} {\mathrm e}^{t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.065 (sec). Leaf size: 57
DSolve[{x'[t]==x[t],y'[t]==y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^t \\ y(t)\to c_2 e^t \\ x(t)\to c_1 e^t \\ y(t)\to 0 \\ x(t)\to 0 \\ y(t)\to c_2 e^t \\ x(t)\to 0 \\ y(t)\to 0 \\ \end{align*}