Internal problem ID [1602]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 10 Linear system of Differential equations. Section 10.4, constant coefficient
homogeneous system. Page 540
Problem number: section 10.4, problem 14.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=3 y_{1} \relax (t )+2 y_{2} \relax (t )-2 y_{3} \relax (t )\\ y_{2}^{\prime }\relax (t )&=-2 y_{1} \relax (t )+7 y_{2} \relax (t )-2 y_{3} \relax (t )\\ y_{3}^{\prime }\relax (t )&=-10 y_{1} \relax (t )+10 y_{2} \relax (t )-5 y_{3} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 66
dsolve([diff(y__1(t),t)=3*y__1(t)+2*y__2(t)-2*y__3(t),diff(y__2(t),t)=-2*y__1(t)+7*y__2(t)-2*y__3(t),diff(y__3(t),t)=-10*y__1(t)+10*y__2(t)-5*y__3(t)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1} \relax (t ) = -\frac {4 c_{2} {\mathrm e}^{5 t}}{5}+\frac {c_{3} {\mathrm e}^{-5 t}}{5}+{\mathrm e}^{5 t} c_{1} \] \[ y_{2} \relax (t ) = \frac {c_{2} {\mathrm e}^{5 t}}{5}+\frac {c_{3} {\mathrm e}^{-5 t}}{5}+{\mathrm e}^{5 t} c_{1} \] \[ y_{3} \relax (t ) = c_{2} {\mathrm e}^{5 t}+c_{3} {\mathrm e}^{-5 t} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 122
DSolve[{y1'[t]==3*y1[t]+2*y2[t]-2*y3[t],y2'[t]==-2*y1[t]+7*y2[t]-2*y3[t],y1'[t]==-10*y1[t]+10*y2[t]-5*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to \frac {1}{64} (c_1-c_2) e^{5 t}-\frac {27 (2 c_1-c_2) e^{25 t/3}}{10648} \\ \text {y2}(t)\to \frac {1}{32} (c_1-c_2) e^{5 t}-\frac {27 (2 c_1-c_2) e^{25 t/3}}{10648} \\ \text {y3}(t)\to \frac {1}{64} (c_1-c_2) e^{5 t}+\frac {45 (2 c_1-c_2) e^{25 t/3}}{10648} \\ \end{align*}