Internal problem ID [1627]
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 24.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (t \right )&=5 y_{1} \left (t \right )-y_{2} \left (t \right )+y_{3} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=-y_{1} \left (t \right )+9 y_{2} \left (t \right )-3 y_{3} \left (t \right )\\ y_{3}^{\prime }\left (t \right )&=-2 y_{1} \left (t \right )+2 y_{2} \left (t \right )+4 y_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 65
dsolve([diff(y__1(t),t)=5*y__1(t)-1*y__2(t)+1*y__3(t),diff(y__2(t),t)=-1*y__1(t)+9*y__2(t)-3*y__3(t),diff(y__3(t),t)=-2*y__1(t)+2*y__2(t)+4*y__3(t)],singsol=all)
\begin{align*} y_{1} \left (t \right ) &= {\mathrm e}^{6 t} \left (c_{3} t +c_{2} \right ) \\ y_{2} \left (t \right ) &= \left (-2 c_{3} t^{2}-4 c_{2} t -3 c_{3} t +c_{1} \right ) {\mathrm e}^{6 t} \\ y_{3} \left (t \right ) &= {\mathrm e}^{6 t} \left (-2 c_{3} t^{2}-4 c_{2} t -2 c_{3} t +c_{1} +c_{2} +c_{3} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 106
DSolve[{y1'[t]==5*y1[t]-1*y2[t]+1*y3[t],y2'[t]==-1*y1[t]+9*y2[t]-3*y3[t],y3'[t]==-2*y1[t]+2*y2[t]+4*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to -e^{6 t} (c_1 (t-1)+(c_2-c_3) t) \\ \text {y2}(t)\to e^{6 t} \left (2 (c_1+c_2-c_3) t^2-(c_1-3 c_2+3 c_3) t+c_2\right ) \\ \text {y3}(t)\to e^{6 t} \left (2 (c_1+c_2-c_3) t^2-2 (c_1-c_2+c_3) t+c_3\right ) \\ \end{align*}