Internal problem ID [1629]
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 26.
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 )-4 y_{3} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=2 y_{1} \left (t \right )-y_{2} \left (t \right )+y_{3} \left (t \right )\\ y_{3}^{\prime }\left (t \right )&=2 y_{1} \left (t \right )+3 y_{2} \left (t \right )+y_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 73
dsolve([diff(y__1(t),t)=-6*y__1(t)-4*y__2(t)-4*y__3(t),diff(y__2(t),t)=2*y__1(t)-1*y__2(t)+1*y__3(t),diff(y__3(t),t)=2*y__1(t)+3*y__2(t)+1*y__3(t)],singsol=all)
\begin{align*} y_{1} \left (t \right ) &= {\mathrm e}^{-2 t} \left (c_{3} t +c_{2} \right ) \\ y_{2} \left (t \right ) &= \frac {\left (2 c_{3} t^{2}+4 c_{2} t -c_{3} t +4 c_{1} \right ) {\mathrm e}^{-2 t}}{4} \\ y_{3} \left (t \right ) &= -\frac {{\mathrm e}^{-2 t} \left (2 c_{3} t^{2}+4 c_{2} t +3 c_{3} t +4 c_{1} +4 c_{2} +c_{3} \right )}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 100
DSolve[{y1'[t]==-6*y1[t]-4*y2[t]-4*y3[t],y2'[t]==2*y1[t]-1*y2[t]+1*y3[t],y3'[t]==2*y1[t]+3*y2[t]+1*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{-2 t} (c_1 (1-4 t)-4 (c_2+c_3) t) \\ \text {y2}(t)\to e^{-2 t} \left (-2 (c_1+c_2+c_3) t^2+(2 c_1+c_2+c_3) t+c_2\right ) \\ \text {y3}(t)\to e^{-2 t} \left (2 (c_1+c_2+c_3) t^2+2 c_1 t+3 (c_2+c_3) t+c_3\right ) \\ \end{align*}