Internal problem ID [335]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.3, The eigenvalue method for linear systems. Page 395
Problem number: problem 21.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )-6 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )-2 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )-2 x_{2} \left (t \right )-4 x_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 54
dsolve([diff(x__1(t),t)=5*x__1(t)+0*x__2(t)-6*x__3(t),diff(x__2(t),t)=2*x__1(t)-1*x__2(t)-2*x__3(t),diff(x__3(t),t)=4*x__1(t)-2*x__2(t)-4*x__3(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{1} +c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{t} \\ x_{2} \left (t \right ) &= \frac {c_{2} {\mathrm e}^{-t}}{2}+\frac {c_{3} {\mathrm e}^{t}}{3}+\frac {c_{1}}{3} \\ x_{3} \left (t \right ) &= c_{2} {\mathrm e}^{-t}+\frac {2 c_{3} {\mathrm e}^{t}}{3}+\frac {5 c_{1}}{6} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 139
DSolve[{x1'[t]==5*x1[t]+0*x2[t]-6*x3[t],x2'[t]==2*x1[t]-1*x2[t]-2*x3[t],x3'[t]==4*x1[t]-2*x2[t]-4*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{-t} \left (c_1 \left (3 e^{2 t}-2\right )+6 \left (e^t-1\right ) \left (c_2 \left (e^t-1\right )-c_3 e^t\right )\right ) \\ \text {x2}(t)\to e^{-t} \left (c_1 \left (e^{2 t}-1\right )+c_2 \left (-4 e^t+2 e^{2 t}+3\right )-2 c_3 e^t \left (e^t-1\right )\right ) \\ \text {x3}(t)\to -2 (c_1-3 c_2) e^{-t}+2 (c_1+2 c_2-2 c_3) e^t+5 (c_3-2 c_2) \\ \end{align*}