Internal problem ID [354]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Examples. Page 437
Problem number: Example 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=9 x_{1} \left (t \right )+4 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-6 x_{1} \left (t \right )-x_{2} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )+4 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 58
dsolve([diff(x__1(t),t)=9*x__1(t)+4*x__2(t)+0*x__3(t),diff(x__2(t),t)=-6*x__1(t)-1*x__2(t)+0*x__3(t),diff(x__3(t),t)=6*x__1(t)+4*x__2(t)+3*x__3(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{2} {\mathrm e}^{3 t}+c_{3} {\mathrm e}^{5 t} \\ x_{2} \left (t \right ) &= -\frac {3 c_{2} {\mathrm e}^{3 t}}{2}-c_{3} {\mathrm e}^{5 t} \\ x_{3} \left (t \right ) &= c_{2} {\mathrm e}^{3 t}+c_{3} {\mathrm e}^{5 t}+c_{1} {\mathrm e}^{3 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 113
DSolve[{x1'[t]==9*x1[t]+4*x2[t]+0*x3[t],x2'[t]==-6*x1[t]-1*x2[t]+0*x3[t],x3'[t]==6*x1[t]+4*x2[t]+3*x[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{3 t} \left (c_1 \left (3 e^{2 t}-2\right )+2 c_2 \left (e^{2 t}-1\right )\right ) \\ \text {x2}(t)\to -e^{3 t} \left (3 c_1 \left (e^{2 t}-1\right )+c_2 \left (2 e^{2 t}-3\right )\right ) \\ \text {x3}(t)\to \int _1^t3 x(K[1])dK[1]+\frac {6}{5} c_1 \left (e^{5 t}-1\right )+\frac {4}{5} c_2 \left (e^{5 t}-1\right )+c_3 \\ \end{align*}