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 }\left (t \right )&=2 y_{2} \left (t \right )+y_{3} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=-4 y_{1} \left (t \right )+6 y_{2} \left (t \right )+y_{3} \left (t \right )\\ y_{3}^{\prime }\left (t \right )&=4 y_{2} \left (t \right )+2 y_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.062 (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)
\[ y_{1} \left (t \right ) = \frac {c_{2} {\mathrm e}^{4 t}}{2}+\frac {c_{3} {\mathrm e}^{4 t} t}{2}-\frac {c_{1}}{2} \] \[ y_{2} \left (t \right ) = \frac {c_{2} {\mathrm e}^{4 t}}{2}+\frac {c_{3} {\mathrm e}^{4 t} t}{2}+\frac {c_{3} {\mathrm e}^{4 t}}{4}-\frac {c_{1}}{2} \] \[ y_{3} \left (t \right ) = c_{1} +c_{2} {\mathrm e}^{4 t}+c_{3} {\mathrm e}^{4 t} t \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 131
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 (c_1 \left (e^{4 t} (2-8 t)+2\right )+e^{4 t} (8 c_2 t+c_3)-c_3\right ) \text {y2}(t)\to \frac {1}{4} \left (-2 c_1 \left (e^{4 t} (4 t+1)-1\right )+e^{4 t} (c_2 (8 t+4)+c_3)-c_3\right ) \text {y3}(t)\to c_1 \left (e^{4 t} (1-4 t)-1\right )+\frac {1}{2} \left (e^{4 t} (8 c_2 t+c_3)+c_3\right ) \end{align*}