Internal problem ID [375]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 18.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )-4 x_{2} \left (t \right )-x_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve([diff(x__1(t),t)=1*x__1(t)+0*x__2(t)-0*x__3(t),diff(x__2(t),t)=1*x__1(t)+3*x__2(t)+1*x__3(t),diff(x__3(t),t)=-2*x__1(t)-4*x__2(t)-1*x__3(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{3} {\mathrm e}^{t} \\ x_{2} \left (t \right ) &= {\mathrm e}^{t} \left (c_{2} t +c_{1} \right ) \\ x_{3} \left (t \right ) &= -{\mathrm e}^{t} \left (2 c_{2} t +2 c_{1} -c_{2} +c_{3} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 54
DSolve[{x1'[t]==1*x1[t]+0*x2[t]-0*x3[t],x2'[t]==1*x1[t]+3*x2[t]+1*x3[t],x3'[t]==-2*x1[t]-4*x2[t]-1*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to c_1 e^t \\ \text {x2}(t)\to e^t ((c_1+2 c_2+c_3) t+c_2) \\ \text {x3}(t)\to e^t (c_3-2 (c_1+2 c_2+c_3) t) \\ \end{align*}