Internal problem ID [1613]
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 10.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=-y_{1}\relax (t )+y_{2}\relax (t )-y_{3}\relax (t )\\ y_{2}^{\prime }\relax (t )&=-2 y_{1}\relax (t )+2 y_{3}\relax (t )\\ y_{3}^{\prime }\relax (t )&=-y_{1}\relax (t )+3 y_{2}\relax (t )-y_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.058 (sec). Leaf size: 60
dsolve([diff(y__1(t),t)=-1*y__1(t)+1*y__2(t)-1*y__3(t),diff(y__2(t),t)=-2*y__1(t)+0*y__2(t)+2*y__3(t),diff(y__3(t),t)=-1*y__1(t)+3*y__2(t)-1*y__3(t)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1}\relax (t ) = \frac {{\mathrm e}^{-2 t} \left (2 c_{3} t +2 c_{2}+c_{3}\right )}{2} \] \[ y_{2}\relax (t ) = c_{1} {\mathrm e}^{2 t}+\frac {c_{3} {\mathrm e}^{-2 t}}{2} \] \[ y_{3}\relax (t ) = c_{1} {\mathrm e}^{2 t}+{\mathrm e}^{-2 t} c_{2}+c_{3} {\mathrm e}^{-2 t} t \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 101
DSolve[{y1'[t]==-1*y1[t]+1*y2[t]-1*y3[t],y2'[t]==-2*y1[t]+0*y2[t]+2*y3[t],y3'[t]==-1*y1[t]+3*y2[t]-1*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{-2 t} (c_1 (t+1)+(c_2-c_3) t) \\ \text {y2}(t)\to c_2 \cosh (2 t)+(c_3-c_1) \sinh (2 t) \\ \text {y3}(t)\to \frac {1}{2} e^{-2 t} \left (2 c_1 t+2 c_2 t-2 c_3 t+(-c_1+c_2+c_3) e^{4 t}+c_1-c_2+c_3\right ) \\ \end{align*}