Internal problem ID [802]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 9.1, The Phase Plane: Linear Systems. page 505
Problem number: 11.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-x_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve([diff(x__1(t),t)=-1*x__1(t)-0*x__2(t),diff(x__2(t),t)=0*x__1(t)-1*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \left (t \right ) = {\mathrm e}^{-t} c_{1} \] \[ x_{2} \left (t \right ) = c_{2} {\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 65
DSolve[{x1'[t]==-1*x1[t]-0*x2[t],x2'[t]==0*x1[t]-1*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to c_1 e^{-t} \text {x2}(t)\to c_2 e^{-t} \text {x1}(t)\to c_1 e^{-t} \text {x2}(t)\to 0 \text {x1}(t)\to 0 \text {x2}(t)\to c_2 e^{-t} \text {x1}(t)\to 0 \text {x2}(t)\to 0 \end{align*}