Internal problem ID [1848]
Book: Differential equations and their applications, 4th ed., M. Braun
Section: Section 3.10, Systems of differential equations. Equal roots. Page 352
Problem number: 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-x_{1} \relax (t )-x_{2} \relax (t )\\ x_{2}^{\prime }\relax (t )&=-x_{2} \relax (t )\\ x_{3}^{\prime }\relax (t )&=-2 x_{3} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 34
dsolve([diff(x__1(t),t)=-1*x__1(t)-1*x__2(t)+0*x__3(t),diff(x__2(t),t)=0*x__1(t)-1*x__2(t)+0*x__3(t),diff(x__3(t),t)=0*x__1(t)-0*x__2(t)-2*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1} \relax (t ) = \left (-c_{2} t +c_{1}\right ) {\mathrm e}^{-t} \] \[ x_{2} \relax (t ) = c_{2} {\mathrm e}^{-t} \] \[ x_{3} \relax (t ) = c_{3} {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 74
DSolve[{x1'[t]==-1*x1[t]-1*x2[t]+0*x3[t],x2'[t]==0*x1[t]-1*x2[t]+0*x3[t],x3'[t]==0*x1[t]-0*x2[t]-2*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{-t} (c_1-c_2 t) \\ \text {x2}(t)\to c_2 e^{-t} \\ \text {x3}(t)\to c_3 e^{-2 t} \\ \text {x1}(t)\to e^{-t} (c_1-c_2 t) \\ \text {x2}(t)\to c_2 e^{-t} \\ \text {x3}(t)\to 0 \\ \end{align*}