Internal problem ID [1834]
Book: Differential equations and their applications, 4th ed., M. Braun
Section: Section 3.8, Systems of differential equations. The eigenva1ue-eigenvector method. Page
339
Problem number: 11.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{1} \relax (t )-3 x_{2} \relax (t )+2 x_{3} \relax (t )\\ x_{2}^{\prime }\relax (t )&=-x_{2} \relax (t )\\ x_{3}^{\prime }\relax (t )&=-x_{2} \relax (t )-2 x_{3} \relax (t ) \end {align*}
With initial conditions \[ [x_{1} \relax (0) = -2, x_{2} \relax (0) = 0, x_{3} \relax (0) = 3] \]
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 24
dsolve([diff(x__1(t),t) = x__1(t)-3*x__2(t)+2*x__3(t), diff(x__2(t),t) = -x__2(t), diff(x__3(t),t) = -x__2(t)-2*x__3(t), x__1(0) = -2, x__2(0) = 0, x__3(0) = 3],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1} \relax (t ) = -2 \,{\mathrm e}^{-2 t} \] \[ x_{2} \relax (t ) = 0 \] \[ x_{3} \relax (t ) = 3 \,{\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 26
DSolve[{x1'[t]==1*x1[t]-3*x2[t]+2*x3[t],x2'[t]==0*x1[t]-1*x2[t]+0*x3[t],x3'[t]==0*x1[t]-1*x2[t]-2*x3[t]},{x1[0]==-2,x2[0]==0,x3[0]==3},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to -2 e^{-2 t} \\ \text {x2}(t)\to 0 \\ \text {x3}(t)\to 3 e^{-2 t} \\ \end{align*}