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 }\relax (t )&=-6 y_{1} \relax (t )-4 y_{2} \relax (t )-4 y_{3} \relax (t )\\ y_{2}^{\prime }\relax (t )&=2 y_{1} \relax (t )-y_{2} \relax (t )+y_{3} \relax (t )\\ y_{3}^{\prime }\relax (t )&=2 y_{1} \relax (t )+3 y_{2} \relax (t )+y_{3} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 67
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)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1} \relax (t ) = -\frac {{\mathrm e}^{-2 t} \left (4 t c_{3}+2 c_{2}-3 c_{3}\right )}{2} \] \[ y_{2} \relax (t ) = -{\mathrm e}^{-2 t} \left (t^{2} c_{3}+c_{2} t -2 t c_{3}+c_{1}-c_{2}+c_{3}\right ) \] \[ y_{3} \relax (t ) = {\mathrm e}^{-2 t} \left (t^{2} c_{3}+c_{2} t +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 95
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} (2 c_1 t (t+1)+(c_2+c_3) t (2 t+3)+c_3) \\ \end{align*}