Internal problem ID [1628]
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 25.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=y_{1}\relax (t )+10 y_{2}\relax (t )-12 y_{3}\relax (t )\\ y_{2}^{\prime }\relax (t )&=2 y_{1}\relax (t )+2 y_{2}\relax (t )+3 y_{3}\relax (t )\\ y_{3}^{\prime }\relax (t )&=2 y_{1}\relax (t )-y_{2}\relax (t )+6 y_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.055 (sec). Leaf size: 77
dsolve([diff(y__1(t),t)=1*y__1(t)+10*y__2(t)-12*y__3(t),diff(y__2(t),t)=2*y__1(t)+2*y__2(t)+3*y__3(t),diff(y__3(t),t)=2*y__1(t)-1*y__2(t)+6*y__3(t)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1}\relax (t ) = -\frac {{\mathrm e}^{3 t} \left (18 c_{3} t^{2}+18 c_{2} t -18 c_{3} t +18 c_{1}-9 c_{2}-c_{3}\right )}{18} \] \[ y_{2}\relax (t ) = \frac {{\mathrm e}^{3 t} \left (9 c_{3} t^{2}+9 c_{2} t +9 c_{1}+c_{3}\right )}{9} \] \[ y_{3}\relax (t ) = {\mathrm e}^{3 t} \left (c_{3} t^{2}+c_{2} t +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 112
DSolve[{y1'[t]==1*y1[t]+10*y2[t]-12*y3[t],y2'[t]==2*y1[t]+2*y2[t]+3*y3[t],y3'[t]==2*y1[t]-1*y2[t]+6*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to -e^{3 t} (c_1 (2 t-1)+c_2 t (9 t-10)+3 c_3 (4-3 t) t) \\ \text {y2}(t)\to e^{3 t} (t (c_2 (9 t-1)+3 c_3 (1-3 t)+2 c_1)+c_2) \\ \text {y3}(t)\to e^{3 t} (t (c_2 (9 t-1)+3 c_3 (1-3 t)+2 c_1)+c_3) \\ \end{align*}