Internal problem ID [339]
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 25.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+2 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-6 x_{1} \left (t \right )-6 x_{2} \left (t \right )-5 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )+6 x_{2} \left (t \right )+5 x_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 111
dsolve([diff(x__1(t),t)=5*x__1(t)+5*x__2(t)+2*x__3(t),diff(x__2(t),t)=-6*x__1(t)-6*x__2(t)-5*x__3(t),diff(x__3(t),t)=6*x__1(t)+6*x__2(t)+5*x__3(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{1} +c_{2} {\mathrm e}^{2 t} \sin \left (3 t \right )+c_{3} {\mathrm e}^{2 t} \cos \left (3 t \right ) \\ x_{2} \left (t \right ) &= -c_{2} {\mathrm e}^{2 t} \sin \left (3 t \right )+c_{2} {\mathrm e}^{2 t} \cos \left (3 t \right )-c_{3} {\mathrm e}^{2 t} \cos \left (3 t \right )-c_{3} {\mathrm e}^{2 t} \sin \left (3 t \right )-c_{1} \\ x_{3} \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{2} \sin \left (3 t \right )+\sin \left (3 t \right ) c_{3} -c_{2} \cos \left (3 t \right )+\cos \left (3 t \right ) c_{3} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 122
DSolve[{x1'[t]==5*x1[t]+5*x2[t]+2*x3[t],x2'[t]==-6*x1[t]-6*x2[t]-5*x3[t],x3'[t]==6*x1[t]+6*x2[t]+5*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to (c_1+c_2+c_3) e^{2 t} \cos (3 t)+(c_1+c_2) e^{2 t} \sin (3 t)-c_2-c_3 \\ \text {x2}(t)\to -c_3 e^{2 t} \cos (3 t)-(2 c_1+2 c_2+c_3) e^{2 t} \sin (3 t)+c_2+c_3 \\ \text {x3}(t)\to e^{2 t} (c_3 \cos (3 t)+(2 c_1+2 c_2+c_3) \sin (3 t)) \\ \end{align*}