Internal problem ID [1599]
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 11.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (t \right )&=y_{1} \left (t \right )-y_{2} \left (t \right )+2 y_{3} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=12 y_{1} \left (t \right )-4 y_{2} \left (t \right )+10 y_{3} \left (t \right )\\ y_{3}^{\prime }\left (t \right )&=-6 y_{1} \left (t \right )+y_{2} \left (t \right )-7 y_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 73
dsolve([diff(y__1(t),t)=1*y__1(t)-1*y__2(t)+2*y__3(t),diff(y__2(t),t)=12*y__1(t)-4*y__2(t)+10*y__3(t),diff(y__3(t),t)=-6*y__1(t)+1*y__2(t)-7*y__3(t)],singsol=all)
\begin{align*} y_{1} \left (t \right ) &= c_{1} {\mathrm e}^{-2 t}+c_{2} {\mathrm e}^{-3 t}+c_{3} {\mathrm e}^{-5 t} \\ y_{2} \left (t \right ) &= c_{1} {\mathrm e}^{-2 t}+2 c_{2} {\mathrm e}^{-3 t}+3 c_{3} {\mathrm e}^{-5 t} \\ y_{3} \left (t \right ) &= -c_{1} {\mathrm e}^{-2 t}-c_{2} {\mathrm e}^{-3 t}-\frac {3 c_{3} {\mathrm e}^{-5 t}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 193
DSolve[{y1'[t]==1*y1[t]-1*y2[t]+2*y3[t],y2'[t]==12*y1[t]-4*y2[t]+10*y3[t],y1'[t]==-6*y1[t]+1*y2[t]-7*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to \frac {e^{-7 t/6} \left (71 (77 c_1-109 c_2) \cos \left (\frac {\sqrt {71} t}{6}\right )+\sqrt {71} (143 c_2-2479 c_1) \sin \left (\frac {\sqrt {71} t}{6}\right )\right )}{340800} \\ \text {y2}(t)\to \frac {e^{-7 t/6} \left (71 (2071 c_1-407 c_2) \cos \left (\frac {\sqrt {71} t}{6}\right )-\sqrt {71} (2717 c_1+5411 c_2) \sin \left (\frac {\sqrt {71} t}{6}\right )\right )}{852000} \\ \text {y3}(t)\to \frac {e^{-7 t/6} \left (639 (23 c_1+9 c_2) \cos \left (\frac {\sqrt {71} t}{6}\right )+3 \sqrt {71} (937 c_1-329 c_2) \sin \left (\frac {\sqrt {71} t}{6}\right )\right )}{568000} \\ \end{align*}