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 }\relax (t )&=y_{1}\relax (t )-y_{2}\relax (t )+2 y_{3}\relax (t )\\ y_{2}^{\prime }\relax (t )&=12 y_{1}\relax (t )-4 y_{2}\relax (t )+10 y_{3}\relax (t )\\ y_{3}^{\prime }\relax (t )&=-6 y_{1}\relax (t )+y_{2}\relax (t )-7 y_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.059 (sec). Leaf size: 74
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)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1}\relax (t ) = -\frac {2 \,{\mathrm e}^{-5 t} c_{1}}{3}-c_{2} {\mathrm e}^{-3 t}-c_{3} {\mathrm e}^{-2 t} \] \[ y_{2}\relax (t ) = -2 \,{\mathrm e}^{-5 t} c_{1}-2 c_{2} {\mathrm e}^{-3 t}-c_{3} {\mathrm e}^{-2 t} \] \[ y_{3}\relax (t ) = {\mathrm e}^{-5 t} c_{1}+c_{2} {\mathrm e}^{-3 t}+c_{3} {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.03 (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*}