Internal problem ID [1827]
Book: Differential equations and their applications, 4th ed., M. Braun
Section: Section 3.8, Systems of differential equations. The eigenva1ue-eigenvector method. Page
339
Problem number: 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=7 x_{1} \left (t \right )-x_{2} \left (t \right )+6 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-10 x_{1} \left (t \right )+4 x_{2} \left (t \right )-12 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 74
dsolve([diff(x__1(t),t)=7*x__1(t)-1*x__2(t)+6*x__3(t),diff(x__2(t),t)=-10*x__1(t)+4*x__2(t)-12*x__3(t),diff(x__3(t),t)=-2*x__1(t)+1*x__2(t)-1*x__3(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{2 t}+c_{3} {\mathrm e}^{5 t} \\ x_{2} \left (t \right ) &= -2 c_{1} {\mathrm e}^{3 t}-c_{2} {\mathrm e}^{2 t}-2 c_{3} {\mathrm e}^{5 t} \\ x_{3} \left (t \right ) &= -c_{1} {\mathrm e}^{3 t}-c_{2} {\mathrm e}^{2 t}-\frac {2 c_{3} {\mathrm e}^{5 t}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 153
DSolve[{x1'[t]==7*x1[t]-1*x2[t]+6*x3[t],x2'[t]==-10*x1[t]+4*x2[t]-12*x3[t],x3'[t]==-2*x1[t]+1*x2[t]-1*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{2 t} \left (c_1 \left (-4 e^t+3 e^{3 t}+2\right )-c_2 \left (e^t-1\right )+3 c_3 e^t \left (e^{2 t}-1\right )\right ) \\ \text {x2}(t)\to -e^{2 t} \left (c_1 \left (-8 e^t+6 e^{3 t}+2\right )+c_2 \left (1-2 e^t\right )+6 c_3 e^t \left (e^{2 t}-1\right )\right ) \\ \text {x3}(t)\to e^{2 t} \left (-2 c_1 \left (-2 e^t+e^{3 t}+1\right )+c_2 \left (e^t-1\right )+c_3 e^t \left (3-2 e^{2 t}\right )\right ) \\ \end{align*}