Internal problem ID [1601]
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 13.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (t \right )&=-2 y_{1} \left (t \right )+2 y_{2} \left (t \right )-6 y_{3} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=2 y_{1} \left (t \right )+6 y_{2} \left (t \right )+2 y_{3} \left (t \right )\\ y_{3}^{\prime }\left (t \right )&=-2 y_{1} \left (t \right )-2 y_{2} \left (t \right )+2 y_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 66
dsolve([diff(y__1(t),t)=-2*y__1(t)+2*y__2(t)-6*y__3(t),diff(y__2(t),t)=2*y__1(t)+6*y__2(t)+2*y__3(t),diff(y__3(t),t)=-2*y__1(t)-2*y__2(t)+2*y__3(t)],singsol=all)
\begin{align*} y_{1} \left (t \right ) &= c_{1} {\mathrm e}^{4 t}+c_{2} {\mathrm e}^{-4 t}+c_{3} {\mathrm e}^{6 t} \\ y_{2} \left (t \right ) &= -\frac {c_{2} {\mathrm e}^{-4 t}}{4}+c_{3} {\mathrm e}^{6 t} \\ y_{3} \left (t \right ) &= -c_{1} {\mathrm e}^{4 t}+\frac {c_{2} {\mathrm e}^{-4 t}}{4}-c_{3} {\mathrm e}^{6 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 257
DSolve[{y1'[t]==-2*y1[t]+2*y2[t]-6*y3[t],y2'[t]==2*y1[t]+6*y2[t]+2*y3[t],y1'[t]==-2*y1[t]-2*y2[t]+2*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to -\frac {e^{-\frac {1}{2} \left (\sqrt {73}-5\right ) t} \left (2 c_1 \left (\left (841 \sqrt {73}-7227\right ) e^{\sqrt {73} t}-7227-841 \sqrt {73}\right )+c_2 \left (\left (171 \sqrt {73}-1825\right ) e^{\sqrt {73} t}-1825-171 \sqrt {73}\right )\right )}{598016} \\ \text {y2}(t)\to \frac {e^{-\frac {1}{2} \left (\sqrt {73}-5\right ) t} \left (c_1 \left (\left (342 \sqrt {73}-3650\right ) e^{\sqrt {73} t}-3650-342 \sqrt {73}\right )-c_2 \left (\left (1971+143 \sqrt {73}\right ) e^{\sqrt {73} t}+1971-143 \sqrt {73}\right )\right )}{598016} \\ \text {y3}(t)\to \frac {e^{-\frac {1}{2} \left (\sqrt {73}-5\right ) t} \left (c_1 \left (\left (342 \sqrt {73}-3650\right ) e^{\sqrt {73} t}-3650-342 \sqrt {73}\right )-c_2 \left (\left (1971+143 \sqrt {73}\right ) e^{\sqrt {73} t}+1971-143 \sqrt {73}\right )\right )}{1196032} \\ \end{align*}