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 }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 73
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)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{3} t +c_{2} \right ) \\ x_{2} \left (t \right ) &= \frac {\left (c_{3} t^{2}+2 c_{2} t -2 c_{3} t +2 c_{1} \right ) {\mathrm e}^{2 t}}{2} \\ x_{3} \left (t \right ) &= -\frac {{\mathrm e}^{2 t} \left (c_{3} t^{2}+2 c_{2} t -4 c_{3} t +2 c_{1} -2 c_{2} -2 c_{3} \right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 110
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} \left (c_2 \left (t^2-2 t+2\right )-(c_1 (t-4) t)+c_3 (t-2) t\right ) \\ \text {x3}(t)\to \frac {1}{2} e^{2 t} \left ((c_1-c_2-c_3) t^2-6 c_1 t+4 (c_2+c_3) t+2 c_3\right ) \\ \end{align*}