Internal problem ID [347]
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 44.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=147 x_{1}\relax (t )+23 x_{2}\relax (t )-202 x_{3}\relax (t )\\ x_{2}^{\prime }\relax (t )&=-90 x_{1}\relax (t )-9 x_{2}\relax (t )+129 x_{3}\relax (t )\\ x_{3}^{\prime }\relax (t )&=90 x_{1}\relax (t )+15 x_{2}\relax (t )-123 x_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.024 (sec). Leaf size: 74
dsolve([diff(x__1(t),t)=147*x__1(t)+23*x__2(t)-202*x__3(t),diff(x__2(t),t)=-90*x__1(t)-9*x__2(t)+129*x__3(t),diff(x__3(t),t)=90*x__1(t)+15*x__2(t)-123*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1}\relax (t ) = \frac {5 c_{1} {\mathrm e}^{12 t}}{3}+\frac {3 c_{2} {\mathrm e}^{-3 t}}{2}+\frac {7 c_{3} {\mathrm e}^{6 t}}{5} \] \[ x_{2}\relax (t ) = -c_{1} {\mathrm e}^{12 t}-c_{2} {\mathrm e}^{-3 t}+\frac {c_{3} {\mathrm e}^{6 t}}{5} \] \[ x_{3}\relax (t ) = c_{1} {\mathrm e}^{12 t}+c_{2} {\mathrm e}^{-3 t}+c_{3} {\mathrm e}^{6 t} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 166
DSolve[{x1'[t]==147*x1[t]+23*x2[t]-202*x3[t],x2'[t]==-90*x1[t]-9*x2[t]+129*x3[t],x3'[t]==90*x1[t]+15*x2[t]-123*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{6} e^{-3 t} \left (5 (12 c_1+c_2-17 c_3) e^{15 t}+7 (c_2+c_3) e^{9 t}-54 c_1-12 c_2+78 c_3\right ) \\ \text {x2}(t)\to \frac {1}{6} e^{-3 t} \left (-3 (12 c_1+c_2-17 c_3) e^{15 t}+(c_2+c_3) e^{9 t}+36 c_1+8 c_2-52 c_3\right ) \\ \text {x3}(t)\to \frac {1}{6} e^{-3 t} \left (3 (12 c_1+c_2-17 c_3) e^{15 t}+5 (c_2+c_3) e^{9 t}-36 c_1-8 c_2+52 c_3\right ) \\ \end{align*}