19.11 problem 11

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 }\relax (t )&=-x_{1} \relax (t )\\ x_{2}^{\prime }\relax (t )&=-x_{2} \relax (t ) \end {align*}

Solution by Maple

Time used: 0.031 (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)
 

\[ x_{1} \relax (t ) = {\mathrm e}^{-t} c_{1} \] \[ x_{2} \relax (t ) = c_{2} {\mathrm e}^{-t} \]

Solution by Mathematica

Time used: 0.038 (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*}