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 }\relax (t )&=-6 y_{1}\relax (t )-4 y_{2}\relax (t )-8 y_{3}\relax (t )\\ y_{2}^{\prime }\relax (t )&=-4 y_{1}\relax (t )-4 y_{3}\relax (t )\\ y_{3}^{\prime }\relax (t )&=-8 y_{1}\relax (t )-4 y_{2}\relax (t )-6 y_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.076 (sec). Leaf size: 66
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)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1}\relax (t ) = -\frac {5 c_{2} {\mathrm e}^{2 t}}{4}+c_{3} {\mathrm e}^{-16 t}-\frac {c_{1} {\mathrm e}^{2 t}}{2} \] \[ y_{2}\relax (t ) = \frac {c_{2} {\mathrm e}^{2 t}}{2}+\frac {c_{3} {\mathrm e}^{-16 t}}{2}+c_{1} {\mathrm e}^{2 t} \] \[ y_{3}\relax (t ) = c_{2} {\mathrm e}^{2 t}+c_{3} {\mathrm e}^{-16 t} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 110
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 {2 (4 c_1+c_2) e^{-16 t}}{44217}-\frac {1}{9} (c_1-2 c_2) e^{2 t} \\ \text {y2}(t)\to \frac {4}{9} (c_1-2 c_2) e^{2 t}+\frac {(4 c_1+c_2) e^{-16 t}}{44217} \\ \text {y3}(t)\to \frac {2 (4 c_1+c_2) e^{-16 t}}{44217}-\frac {1}{9} (c_1-2 c_2) e^{2 t} \\ \end{align*}