Internal problem ID [1615]
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 12.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=6 y_{1} \relax (t )-5 y_{2} \relax (t )+3 y_{3} \relax (t )\\ y_{2}^{\prime }\relax (t )&=2 y_{1} \relax (t )-y_{2} \relax (t )+3 y_{3} \relax (t )\\ y_{3}^{\prime }\relax (t )&=2 y_{1} \relax (t )+y_{2} \relax (t )+y_{3} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 80
dsolve([diff(y__1(t),t)=6*y__1(t)-5*y__2(t)+3*y__3(t),diff(y__2(t),t)=2*y__1(t)-1*y__2(t)+3*y__3(t),diff(y__3(t),t)=2*y__1(t)+1*y__2(t)+1*y__3(t)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1} \relax (t ) = -c_{1} {\mathrm e}^{-2 t}+c_{2} {\mathrm e}^{4 t}+c_{3} {\mathrm e}^{4 t} t +\frac {c_{3} {\mathrm e}^{4 t}}{2} \] \[ y_{2} \relax (t ) = -c_{1} {\mathrm e}^{-2 t}+c_{2} {\mathrm e}^{4 t}+c_{3} {\mathrm e}^{4 t} t \] \[ y_{3} \relax (t ) = c_{1} {\mathrm e}^{-2 t}+c_{2} {\mathrm e}^{4 t}+c_{3} {\mathrm e}^{4 t} t \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 127
DSolve[{y1'[t]==6*y1[t]-5*y2[t]+3*y3[t],y2'[t]==2*y1[t]-1*y2[t]+3*y3[t],y3'[t]==2*y1[t]+1*y2[t]+1*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to \frac {1}{2} e^{-2 t} \left (e^{6 t} (c_1 (4 t+2)-c_2 (4 t+1)+c_3)+c_2-c_3\right ) \\ \text {y2}(t)\to \frac {1}{2} e^{-2 t} \left (e^{6 t} (4 (c_1-c_2) t+c_2+c_3)+c_2-c_3\right ) \\ \text {y3}(t)\to \frac {1}{2} e^{-2 t} \left (e^{6 t} (4 (c_1-c_2) t+c_2+c_3)-c_2+c_3\right ) \\ \end{align*}