Internal problem ID [1624]
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 21.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=-y_{1}\relax (t )-4 y_{2}\relax (t )-y_{3}\relax (t )\\ y_{2}^{\prime }\relax (t )&=3 y_{1}\relax (t )+6 y_{2}\relax (t )+y_{3}\relax (t )\\ y_{3}^{\prime }\relax (t )&=-3 y_{1}\relax (t )-2 y_{2}\relax (t )+3 y_{3}\relax (t ) \end {align*}
With initial conditions \[ [y_{1}\relax (0) = -2, y_{2}\relax (0) = 1, y_{3}\relax (0) = 3] \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 63
dsolve([diff(y__1(t),t) = -y__1(t)-4*y__2(t)-y__3(t), diff(y__2(t),t) = 3*y__1(t)+6*y__2(t)+y__3(t), diff(y__3(t),t) = -3*y__1(t)-2*y__2(t)+3*y__3(t), y__1(0) = -2, y__2(0) = 1, y__3(0) = 3],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1}\relax (t ) = -2 \,{\mathrm e}^{4 t}+3 \,{\mathrm e}^{2 t} t \] \[ y_{2}\relax (t ) = 2 \,{\mathrm e}^{4 t}-{\mathrm e}^{2 t}-3 \,{\mathrm e}^{2 t} t \] \[ y_{3}\relax (t ) = 2 \,{\mathrm e}^{4 t}+{\mathrm e}^{2 t}+3 \,{\mathrm e}^{2 t} t \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 63
DSolve[{y1'[t]==-1*y1[t]-4*y2[t]-1*y3[t],y2'[t]==3*y1[t]+6*y2[t]+1*y3[t],y3'[t]==-3*y1[t]-2*y2[t]+3*y3[t]},{y1[0]==-2,y2[0]==1,y3[0]==3},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to 3 e^{2 t} t-2 e^{4 t} \\ \text {y2}(t)\to e^{2 t} \left (-3 t+2 e^{2 t}-1\right ) \\ \text {y3}(t)\to e^{2 t} \left (3 t+2 e^{2 t}+1\right ) \\ \end{align*}