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 }\relax (t )&=x_{1}\relax (t )+2 x_{2}\relax (t )+2 x_{3}\relax (t )\\ x_{2}^{\prime }\relax (t )&=2 x_{1}\relax (t )+7 x_{2}\relax (t )+x_{3}\relax (t )\\ x_{3}^{\prime }\relax (t )&=2 x_{1}\relax (t )+x_{2}\relax (t )+7 x_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.017 (sec). Leaf size: 51
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)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1}\relax (t ) = \frac {c_{3} {\mathrm e}^{9 t}}{2}-4 c_{1} \] \[ x_{2}\relax (t ) = -c_{2} {\mathrm e}^{6 t}+c_{3} {\mathrm e}^{9 t}+c_{1} \] \[ x_{3}\relax (t ) = c_{1}+c_{2} {\mathrm e}^{6 t}+c_{3} {\mathrm e}^{9 t} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 128
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 (9 (c_2-c_3) e^{6 t}+4 (c_1+2 (c_2+c_3)) e^{9 t}-4 c_1+c_2+c_3\right ) \\ \text {x3}(t)\to \frac {1}{18} \left (-9 (c_2-c_3) e^{6 t}+4 (c_1+2 (c_2+c_3)) e^{9 t}-4 c_1+c_2+c_3\right ) \\ \end{align*}