Internal problem ID [332]
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 18.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )+7 x_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 54
dsolve([diff(x__1(t),t)=x__1(t)+2*x__2(t)+2*x__3(t),diff(x__2(t),t)=2*x__1(t)+7*x__2(t)+x__3(t),diff(x__3(t),t)=2*x__1(t)+x__2(t)+7*x__3(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{2} +c_{3} {\mathrm e}^{9 t} \\ x_{2} \left (t \right ) &= 2 c_{3} {\mathrm e}^{9 t}+{\mathrm e}^{6 t} c_{1} -\frac {c_{2}}{4} \\ x_{3} \left (t \right ) &= 2 c_{3} {\mathrm e}^{9 t}-{\mathrm e}^{6 t} c_{1} -\frac {c_{2}}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 148
DSolve[{x1'[t]==x1[t]+2*x2[t]+2*x3[t],x2'[t]==2*x1[t]+7*x2[t]+x3[t],x3'[t]==2*x1[t]+x2[t]+7*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{9} \left (c_1 \left (e^{9 t}+8\right )+2 (c_2+c_3) \left (e^{9 t}-1\right )\right ) \\ \text {x2}(t)\to \frac {1}{18} \left (4 c_1 \left (e^{9 t}-1\right )+c_2 \left (9 e^{6 t}+8 e^{9 t}+1\right )+c_3 \left (-9 e^{6 t}+8 e^{9 t}+1\right )\right ) \\ \text {x3}(t)\to \frac {1}{18} \left (4 c_1 \left (e^{9 t}-1\right )+c_2 \left (-9 e^{6 t}+8 e^{9 t}+1\right )+c_3 \left (9 e^{6 t}+8 e^{9 t}+1\right )\right ) \\ \end{align*}