Internal problem ID [1630]
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 27.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=2 y_{2} \relax (t )-2 y_{3} \relax (t )\\ y_{2}^{\prime }\relax (t )&=-y_{1} \relax (t )+5 y_{2} \relax (t )-3 y_{3} \relax (t )\\ y_{3}^{\prime }\relax (t )&=y_{1} \relax (t )+y_{2} \relax (t )+y_{3} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 71
dsolve([diff(y__1(t),t)=0*y__1(t)+2*y__2(t)-2*y__3(t),diff(y__2(t),t)=-1*y__1(t)+5*y__2(t)-3*y__3(t),diff(y__3(t),t)=1*y__1(t)+1*y__2(t)+1*y__3(t)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1} \relax (t ) = \frac {{\mathrm e}^{2 t} \left (4 t c_{3}+2 c_{2}-c_{3}\right )}{4} \] \[ y_{2} \relax (t ) = \frac {{\mathrm e}^{2 t} \left (4 t^{2} c_{3}+4 c_{2} t +4 t c_{3}+4 c_{1}+2 c_{2}+c_{3}\right )}{4} \] \[ y_{3} \relax (t ) = {\mathrm e}^{2 t} \left (t^{2} c_{3}+c_{2} t +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 100
DSolve[{y1'[t]==0*y1[t]+2*y2[t]-2*y3[t],y2'[t]==-1*y1[t]+5*y2[t]-3*y3[t],y3'[t]==1*y1[t]+1*y2[t]+1*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{2 t} (-2 c_1 t+2 c_2 t-2 c_3 t+c_1) \\ \text {y2}(t)\to e^{2 t} (c_1 (-t) (2 t+1)+(c_2-c_3) t (2 t+3)+c_2) \\ \text {y3}(t)\to e^{2 t} (c_1 (1-2 t) t+(c_2-c_3) t (2 t+1)+c_3) \\ \end{align*}