Internal problem ID [1847]
Book: Differential equations and their applications, 4th ed., M. Braun
Section: Section 3.10, Systems of differential equations. Equal roots. Page 352
Problem number: 2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{1}\relax (t )+x_{2}\relax (t )+x_{3}\relax (t )\\ x_{2}^{\prime }\relax (t )&=2 x_{1}\relax (t )+x_{2}\relax (t )-x_{3}\relax (t )\\ x_{3}^{\prime }\relax (t )&=-3 x_{1}\relax (t )+2 x_{2}\relax (t )+4 x_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.054 (sec). Leaf size: 65
dsolve([diff(x__1(t),t)=1*x__1(t)+1*x__2(t)+1*x__3(t),diff(x__2(t),t)=2*x__1(t)+1*x__2(t)-1*x__3(t),diff(x__3(t),t)=-3*x__1(t)+2*x__2(t)+4*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1}\relax (t ) = -{\mathrm e}^{2 t} \left (2 c_{3} t +c_{2}+4 c_{3}\right ) \] \[ x_{2}\relax (t ) = -{\mathrm e}^{2 t} \left (c_{3} t^{2}+c_{2} t +2 c_{3} t +c_{1}+c_{2}+6 c_{3}\right ) \] \[ x_{3}\relax (t ) = {\mathrm e}^{2 t} \left (c_{3} t^{2}+c_{2} t +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 96
DSolve[{x1'[t]==1*x1[t]+1*x2[t]+1*x3[t],x2'[t]==2*x1[t]+1*x2[t]-1*x3[t],x3'[t]==-3*x1[t]+2*x2[t]+4*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{2 t} ((c_2+c_3) t-c_1 (t-1)) \\ \text {x2}(t)\to \frac {1}{2} e^{2 t} (-(c_1 (t-4) t)+(c_2+c_3) (t-2) t+2 c_2) \\ \text {x3}(t)\to \frac {1}{2} e^{2 t} (c_1 (t-6) t-(c_2+c_3) (t-4) t+2 c_3) \\ \end{align*}