Internal problem ID [1630]
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 27.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (t \right )&=2 y_{2} \left (t \right )-2 y_{3} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=-y_{1} \left (t \right )+5 y_{2} \left (t \right )-3 y_{3} \left (t \right )\\ y_{3}^{\prime }\left (t \right )&=y_{1} \left (t \right )+y_{2} \left (t \right )+y_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 74
dsolve([diff(y__1(t),t)=0*y__1(t)+2*y__2(t)-2*y__3(t),diff(y__2(t),t)=-1*y__1(t)+5*y__2(t)-3*y__3(t),diff(y__3(t),t)=1*y__1(t)+1*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 +3 c_{3} t +2 c_{1} \right ) {\mathrm e}^{2 t}}{2} \\ y_{3} \left (t \right ) &= \frac {{\mathrm e}^{2 t} \left (2 c_{3} t^{2}+4 c_{2} t +c_{3} t +2 c_{1} -2 c_{2} -c_{3} \right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 108
DSolve[{y1'[t]==0*y1[t]+2*y2[t]-2*y3[t],y2'[t]==-1*y1[t]+5*y2[t]-3*y3[t],y3'[t]==1*y1[t]+1*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 (2 t-1)+2 (c_3-c_2) t) \\ \text {y2}(t)\to e^{2 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^{2 t} \left (-2 (c_1-c_2+c_3) t^2+(c_1+c_2-c_3) t+c_3\right ) \\ \end{align*}