Internal problem ID [1628]
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 25.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (t \right )&=y_{1} \left (t \right )+10 y_{2} \left (t \right )-12 y_{3} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=2 y_{1} \left (t \right )+2 y_{2} \left (t \right )+3 y_{3} \left (t \right )\\ y_{3}^{\prime }\left (t \right )&=2 y_{1} \left (t \right )-y_{2} \left (t \right )+6 y_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 86
dsolve([diff(y__1(t),t)=1*y__1(t)+10*y__2(t)-12*y__3(t),diff(y__2(t),t)=2*y__1(t)+2*y__2(t)+3*y__3(t),diff(y__3(t),t)=2*y__1(t)-1*y__2(t)+6*y__3(t)],singsol=all)
\begin{align*} y_{1} \left (t \right ) &= {\mathrm e}^{3 t} \left (c_{3} t^{2}+c_{2} t +c_{1} \right ) \\ y_{2} \left (t \right ) &= -\frac {{\mathrm e}^{3 t} \left (6 c_{3} t^{2}+6 c_{2} t +6 c_{3} t +6 c_{1} +3 c_{2} +4 c_{3} \right )}{6} \\ y_{3} \left (t \right ) &= -\frac {{\mathrm e}^{3 t} \left (18 c_{3} t^{2}+18 c_{2} t +18 c_{3} t +18 c_{1} +9 c_{2} +10 c_{3} \right )}{18} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 118
DSolve[{y1'[t]==1*y1[t]+10*y2[t]-12*y3[t],y2'[t]==2*y1[t]+2*y2[t]+3*y3[t],y3'[t]==2*y1[t]-1*y2[t]+6*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to -e^{3 t} (c_1 (2 t-1)+c_2 t (9 t-10)+3 c_3 (4-3 t) t) \\ \text {y2}(t)\to e^{3 t} \left (9 (c_2-c_3) t^2+(2 c_1-c_2+3 c_3) t+c_2\right ) \\ \text {y3}(t)\to e^{3 t} \left (9 (c_2-c_3) t^2+(2 c_1-c_2+3 c_3) t+c_3\right ) \\ \end{align*}