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 }\relax (t )&=5 x_{1}\relax (t )+5 x_{2}\relax (t )+2 x_{3}\relax (t )\\ x_{2}^{\prime }\relax (t )&=-6 x_{1}\relax (t )-6 x_{2}\relax (t )-5 x_{3}\relax (t )\\ x_{3}^{\prime }\relax (t )&=6 x_{1}\relax (t )+6 x_{2}\relax (t )+5 x_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 101
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)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1}\relax (t ) = \frac {c_{2} {\mathrm e}^{2 t} \sin \left (3 t \right )}{2}+\frac {c_{2} {\mathrm e}^{2 t} \cos \left (3 t \right )}{2}+\frac {c_{3} {\mathrm e}^{2 t} \cos \left (3 t \right )}{2}-\frac {c_{3} {\mathrm e}^{2 t} \sin \left (3 t \right )}{2}-c_{1} \] \[ x_{2}\relax (t ) = -c_{2} {\mathrm e}^{2 t} \sin \left (3 t \right )-c_{3} {\mathrm e}^{2 t} \cos \left (3 t \right )+c_{1} \] \[ x_{3}\relax (t ) = {\mathrm e}^{2 t} \left (c_{2} \sin \left (3 t \right )+c_{3} \cos \left (3 t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 114
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 e^{2 t} ((c_1+c_2+c_3) \cos (3 t)+(c_1+c_2) \sin (3 t))-c_2-c_3 \\ \text {x2}(t)\to e^{2 t} (-c_3 \cos (3 t)-(2 (c_1+c_2)+c_3) \sin (3 t))+c_2+c_3 \\ \text {x3}(t)\to e^{2 t} (c_3 \cos (3 t)+(2 (c_1+c_2)+c_3) \sin (3 t)) \\ \end{align*}