Internal problem ID [1632]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 10 Linear system of Differential equations. Section 10.5, constant coefficient
homogeneous system II. Page 555
Problem number: section 10.5, problem 29.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (t \right )&=-y_{1} \left (t \right )-12 y_{2} \left (t \right )+8 y_{3} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=y_{1} \left (t \right )-9 y_{2} \left (t \right )+4 y_{3} \left (t \right )\\ y_{3}^{\prime }\left (t \right )&=y_{1} \left (t \right )-6 y_{2} \left (t \right )+y_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 53
dsolve([diff(y__1(t),t)=-1*y__1(t)-12*y__2(t)+8*y__3(t),diff(y__2(t),t)=1*y__1(t)-9*y__2(t)+4*y__3(t),diff(y__3(t),t)=1*y__1(t)-6*y__2(t)+1*y__3(t)],singsol=all)
\begin{align*} y_{1} \left (t \right ) &= {\mathrm e}^{-3 t} \left (c_{3} t +c_{2} \right ) \\ y_{2} \left (t \right ) &= \frac {{\mathrm e}^{-3 t} \left (c_{3} t +2 c_{1} +c_{2} \right )}{2} \\ y_{3} \left (t \right ) &= \frac {{\mathrm e}^{-3 t} \left (4 c_{3} t +12 c_{1} +4 c_{2} +c_{3} \right )}{8} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 79
DSolve[{y1'[t]==-1*y1[t]-12*y2[t]+8*y3[t],y2'[t]==1*y1[t]-9*y2[t]+4*y3[t],y3'[t]==1*y1[t]-6*y2[t]+1*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{-3 t} (2 c_1 t-12 c_2 t+8 c_3 t+c_1) \\ \text {y2}(t)\to e^{-3 t} ((c_1-6 c_2+4 c_3) t+c_2) \\ \text {y3}(t)\to e^{-3 t} ((c_1-6 c_2+4 c_3) t+c_3) \\ \end{align*}