Internal problem ID [1631]
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 28.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=-2 y_{1} \relax (t )-12 y_{2} \relax (t )+10 y_{3} \relax (t )\\ y_{2}^{\prime }\relax (t )&=2 y_{1} \relax (t )-24 y_{2} \relax (t )+11 y_{3} \relax (t )\\ y_{3}^{\prime }\relax (t )&=2 y_{1} \relax (t )-24 y_{2} \relax (t )+8 y_{3} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 86
dsolve([diff(y__1(t),t)=-2*y__1(t)-12*y__2(t)+10*y__3(t),diff(y__2(t),t)=2*y__1(t)-24*y__2(t)+11*y__3(t),diff(y__3(t),t)=2*y__1(t)-24*y__2(t)+8*y__3(t)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1} \relax (t ) = -\frac {{\mathrm e}^{-6 t} \left (6 t^{2} c_{3}+6 c_{2} t +6 t c_{3}+6 c_{1}+3 c_{2}+2 c_{3}\right )}{6} \] \[ y_{2} \relax (t ) = \frac {{\mathrm e}^{-6 t} \left (18 t^{2} c_{3}+18 c_{2} t -6 t c_{3}+18 c_{1}-3 c_{2}-c_{3}\right )}{36} \] \[ y_{3} \relax (t ) = {\mathrm e}^{-6 t} \left (t^{2} c_{3}+c_{2} t +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 125
DSolve[{y1'[t]==-2*y1[t]-12*y2[t]+10*y3[t],y2'[t]==2*y1[t]-24*y2[t]+11*y3[t],y3'[t]==2*y1[t]-24*y2[t]+8*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{-6 t} \left (c_1 \left (6 t^2+4 t+1\right )+2 t (c_3 (12 t+5)-6 c_2 (3 t+1))\right ) \\ \text {y2}(t)\to e^{-6 t} (t (c_1 (2-3 t)+18 c_2 (t-1)+c_3 (11-12 t))+c_2) \\ \text {y3}(t)\to e^{-6 t} (2 t (c_1 (1-3 t)+6 c_2 (3 t-2)+c_3 (7-12 t))+c_3) \\ \end{align*}