Internal problem ID [370]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 13.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{2} \left (t \right )-4 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=x_{2} \left (t \right )-3 x_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 54
dsolve([diff(x__1(t),t)=-1*x__1(t)+0*x__2(t)+1*x__3(t),diff(x__2(t),t)=0*x__1(t)+1*x__2(t)-4*x__3(t),diff(x__3(t),t)=0*x__1(t)+1*x__2(t)-3*x__3(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= \frac {\left (c_{3} t^{2}+2 c_{2} t +2 c_{1} \right ) {\mathrm e}^{-t}}{2} \\ x_{2} \left (t \right ) &= {\mathrm e}^{-t} \left (2 c_{3} t +2 c_{2} +c_{3} \right ) \\ x_{3} \left (t \right ) &= {\mathrm e}^{-t} \left (c_{3} t +c_{2} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 78
DSolve[{x1'[t]==-1*x1[t]+0*x2[t]+1*x3[t],x2'[t]==0*x1[t]+1*x2[t]-4*x3[t],x3'[t]==0*x1[t]+1*x2[t]-3*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{2} e^{-t} (t ((c_2-2 c_3) t+2 c_3)+2 c_1) \\ \text {x2}(t)\to e^{-t} (2 c_2 t-4 c_3 t+c_2) \\ \text {x3}(t)\to e^{-t} ((c_2-2 c_3) t+c_3) \\ \end{align*}