Internal problem ID [1597]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 10 Linear system of Differential equations. Section 10.4, constant coefficient
homogeneous system. Page 540
Problem number: section 10.4, problem 9.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (t \right )&=-6 y_{1} \left (t \right )-4 y_{2} \left (t \right )-8 y_{3} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=-4 y_{1} \left (t \right )-4 y_{3} \left (t \right )\\ y_{3}^{\prime }\left (t \right )&=-8 y_{1} \left (t \right )-4 y_{2} \left (t \right )-6 y_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 67
dsolve([diff(y__1(t),t)=-6*y__1(t)-4*y__2(t)-8*y__3(t),diff(y__2(t),t)=-4*y__1(t)-0*y__2(t)-4*y__3(t),diff(y__3(t),t)=-8*y__1(t)-4*y__2(t)-6*y__3(t)],singsol=all)
\begin{align*} y_{1} \left (t \right ) &= 2 c_{2} {\mathrm e}^{-16 t}+2 c_{3} {\mathrm e}^{2 t}+c_{1} {\mathrm e}^{2 t} \\ y_{2} \left (t \right ) &= c_{2} {\mathrm e}^{-16 t}+c_{3} {\mathrm e}^{2 t} \\ y_{3} \left (t \right ) &= 2 c_{2} {\mathrm e}^{-16 t}-\frac {5 c_{3} {\mathrm e}^{2 t}}{2}-c_{1} {\mathrm e}^{2 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 116
DSolve[{y1'[t]==-6*y1[t]-4*y2[t]-8*y3[t],y2'[t]==-4*y1[t]-0*y2[t]-4*y3[t],y1'[t]==-8*y1[t]-4*y2[t]-6*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to \frac {e^{-16 t} \left (c_1 \left (8-4913 e^{18 t}\right )+2 c_2 \left (4913 e^{18 t}+1\right )\right )}{44217} \\ \text {y2}(t)\to \frac {e^{-16 t} \left (4 c_1 \left (4913 e^{18 t}+1\right )+c_2 \left (1-39304 e^{18 t}\right )\right )}{44217} \\ \text {y3}(t)\to \frac {e^{-16 t} \left (c_1 \left (8-4913 e^{18 t}\right )+2 c_2 \left (4913 e^{18 t}+1\right )\right )}{44217} \\ \end{align*}