Internal problem ID [1633]
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 30.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=-4 y_{1}\relax (t )-y_{3}\relax (t )\\ y_{2}^{\prime }\relax (t )&=-y_{1}\relax (t )-3 y_{2}\relax (t )-y_{3}\relax (t )\\ y_{3}^{\prime }\relax (t )&=y_{1}\relax (t )-2 y_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.054 (sec). Leaf size: 49
dsolve([diff(y__1(t),t)=-4*y__1(t)-0*y__2(t)-1*y__3(t),diff(y__2(t),t)=-1*y__1(t)-3*y__2(t)-1*y__3(t),diff(y__3(t),t)=1*y__1(t)-0*y__2(t)-2*y__3(t)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1}\relax (t ) = -{\mathrm e}^{-3 t} \left (c_{3} t +c_{2}-c_{3}\right ) \] \[ y_{2}\relax (t ) = {\mathrm e}^{-3 t} \left (-c_{3} t +c_{1}-c_{2}\right ) \] \[ y_{3}\relax (t ) = {\mathrm e}^{-3 t} \left (c_{3} t +c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 63
DSolve[{y1'[t]==-4*y1[t]-0*y2[t]-1*y3[t],y2'[t]==-1*y1[t]-3*y2[t]-1*y3[t],y3'[t]==1*y1[t]-0*y2[t]-2*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{-3 t} (c_1 (-t)-c_3 t+c_1) \\ \text {y2}(t)\to e^{-3 t} (c_2-(c_1+c_3) t) \\ \text {y3}(t)\to e^{-3 t} ((c_1+c_3) t+c_3) \\ \end{align*}