Internal problem ID [1850]
Book: Differential equations and their applications, 4th ed., M. Braun
Section: Section 3.10, Systems of differential equations. Equal roots. Page 352
Problem number: 5.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-x_{1} \relax (t )+x_{2} \relax (t )+2 x_{3} \relax (t )\\ x_{2}^{\prime }\relax (t )&=-x_{1} \relax (t )+x_{2} \relax (t )+x_{3} \relax (t )\\ x_{3}^{\prime }\relax (t )&=-2 x_{1} \relax (t )+x_{2} \relax (t )+3 x_{3} \relax (t ) \end {align*}
With initial conditions \[ [x_{1} \relax (0) = 1, x_{2} \relax (0) = 0, x_{3} \relax (0) = 1] \]
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 16
dsolve([diff(x__1(t),t) = -x__1(t)+x__2(t)+2*x__3(t), diff(x__2(t),t) = -x__1(t)+x__2(t)+x__3(t), diff(x__3(t),t) = -2*x__1(t)+x__2(t)+3*x__3(t), x__1(0) = 1, x__2(0) = 0, x__3(0) = 1],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1} \relax (t ) = {\mathrm e}^{t} \] \[ x_{2} \relax (t ) = 0 \] \[ x_{3} \relax (t ) = {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 18
DSolve[{x1'[t]==-1*x1[t]+1*x2[t]+2*x3[t],x2'[t]==-1*x1[t]+1*x2[t]+1*x3[t],x3'[t]==-2*x1[t]+1*x2[t]+3*x3[t]},{x1[0]==1,x2[0]==0,x3[0]==1},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^t \\ \text {x2}(t)\to 0 \\ \text {x3}(t)\to e^t \\ \end{align*}