Internal problem ID [1603]
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 15.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=3 y_{1} \relax (t )+y_{2} \relax (t )-y_{3} \relax (t )\\ y_{2}^{\prime }\relax (t )&=3 y_{1} \relax (t )+5 y_{2} \relax (t )+y_{3} \relax (t )\\ y_{3}^{\prime }\relax (t )&=-6 y_{1} \relax (t )+2 y_{2} \relax (t )+4 y_{3} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 54
dsolve([diff(y__1(t),t)=3*y__1(t)+1*y__2(t)-1*y__3(t),diff(y__2(t),t)=3*y__1(t)+5*y__2(t)+1*y__3(t),diff(y__3(t),t)=-6*y__1(t)+2*y__2(t)+4*y__3(t)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1} \relax (t ) = -\frac {c_{3} {\mathrm e}^{6 t}}{2}+\frac {c_{2}}{2}+\frac {c_{1} {\mathrm e}^{6 t}}{3} \] \[ y_{2} \relax (t ) = -\frac {c_{2}}{2}-\frac {c_{3} {\mathrm e}^{6 t}}{2}+c_{1} {\mathrm e}^{6 t} \] \[ y_{3} \relax (t ) = c_{2}+c_{3} {\mathrm e}^{6 t} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 91
DSolve[{y1'[t]==3*y1[t]+1*y2[t]-1*y3[t],y2'[t]==3*y1[t]+5*y2[t]+1*y3[t],y1'[t]==-6*y1[t]+2*y2[t]+4*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to -\frac {1}{625} (c_1+c_2) e^{6 t}+\frac {4 c_1}{5}-\frac {c_2}{5} \\ \text {y2}(t)\to \frac {1}{5} (c_2-4 c_1)-\frac {4}{625} (c_1+c_2) e^{6 t} \\ \text {y3}(t)\to -\frac {1}{625} (c_1+c_2) e^{6 t}+\frac {8 c_1}{5}-\frac {2 c_2}{5} \\ \end{align*}