Internal problem ID [1611]
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 8.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=2 y_{2} \relax (t )+y_{3} \relax (t )\\ y_{2}^{\prime }\relax (t )&=-4 y_{1} \relax (t )+6 y_{2} \relax (t )+y_{3} \relax (t )\\ y_{3}^{\prime }\relax (t )&=4 y_{2} \relax (t )+2 y_{3} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 71
dsolve([diff(y__1(t),t)=0*y__1(t)+2*y__2(t)+1*y__3(t),diff(y__2(t),t)=-4*y__1(t)+6*y__2(t)+1*y__3(t),diff(y__3(t),t)=0*y__1(t)+4*y__2(t)+2*y__3(t)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1} \relax (t ) = \frac {c_{2} {\mathrm e}^{4 t}}{2}+\frac {c_{3} {\mathrm e}^{4 t} t}{2}-\frac {c_{1}}{2} \] \[ y_{2} \relax (t ) = \frac {c_{2} {\mathrm e}^{4 t}}{2}+\frac {c_{3} {\mathrm e}^{4 t} t}{2}+\frac {c_{3} {\mathrm e}^{4 t}}{4}-\frac {c_{1}}{2} \] \[ y_{3} \relax (t ) = c_{1}+c_{2} {\mathrm e}^{4 t}+c_{3} {\mathrm e}^{4 t} t \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 118
DSolve[{y1'[t]==0*y1[t]+2*y2[t]+1*y3[t],y2'[t]==-4*y1[t]+6*y2[t]+1*y3[t],y3'[t]==0*y1[t]+4*y2[t]+2*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to \frac {1}{4} \left (e^{4 t} (c_1 (2-8 t)+8 c_2 t+c_3)+2 c_1-c_3\right ) \\ \text {y2}(t)\to \frac {1}{4} \left (e^{4 t} (-2 c_1 (4 t+1)+c_2 (8 t+4)+c_3)+2 c_1-c_3\right ) \\ \text {y3}(t)\to \frac {1}{2} \left (e^{4 t} (c_1 (2-8 t)+8 c_2 t+c_3)-2 c_1+c_3\right ) \\ \end{align*}