Internal problem ID [1627]
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 24.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=5 y_{1}\relax (t )-y_{2}\relax (t )+y_{3}\relax (t )\\ y_{2}^{\prime }\relax (t )&=-y_{1}\relax (t )+9 y_{2}\relax (t )-3 y_{3}\relax (t )\\ y_{3}^{\prime }\relax (t )&=-2 y_{1}\relax (t )+2 y_{2}\relax (t )+4 y_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.06 (sec). Leaf size: 67
dsolve([diff(y__1(t),t)=5*y__1(t)-1*y__2(t)+1*y__3(t),diff(y__2(t),t)=-1*y__1(t)+9*y__2(t)-3*y__3(t),diff(y__3(t),t)=-2*y__1(t)+2*y__2(t)+4*y__3(t)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1}\relax (t ) = -\frac {{\mathrm e}^{6 t} \left (2 c_{3} t +c_{2}-c_{3}\right )}{4} \] \[ y_{2}\relax (t ) = \frac {{\mathrm e}^{6 t} \left (4 c_{3} t^{2}+4 c_{2} t +2 c_{3} t +4 c_{1}+c_{2}+c_{3}\right )}{4} \] \[ y_{3}\relax (t ) = {\mathrm e}^{6 t} \left (c_{3} t^{2}+c_{2} t +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 96
DSolve[{y1'[t]==5*y1[t]-1*y2[t]+1*y3[t],y2'[t]==-1*y1[t]+9*y2[t]-3*y3[t],y3'[t]==-2*y1[t]+2*y2[t]+4*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{6 t} (c_1 (-t)-c_2 t+c_3 t+c_1) \\ \text {y2}(t)\to e^{6 t} (c_1 t (2 t-1)+(c_2-c_3) t (2 t+3)+c_2) \\ \text {y3}(t)\to e^{6 t} (2 t (c_1 (t-1)+(c_2-c_3) (t+1))+c_3) \\ \end{align*}