Internal problem ID [1625]
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 22.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=4 y_{1}\relax (t )-8 y_{2}\relax (t )-4 y_{3}\relax (t )\\ y_{2}^{\prime }\relax (t )&=-3 y_{1}\relax (t )-y_{2}\relax (t )-4 y_{3}\relax (t )\\ y_{3}^{\prime }\relax (t )&=y_{1}\relax (t )-y_{2}\relax (t )+9 y_{3}\relax (t ) \end {align*}
With initial conditions \[ [y_{1}\relax (0) = -4, y_{2}\relax (0) = 1, y_{3}\relax (0) = -3] \]
✓ Solution by Maple
Time used: 0.085 (sec). Leaf size: 62
dsolve([diff(y__1(t),t) = 4*y__1(t)-8*y__2(t)-4*y__3(t), diff(y__2(t),t) = -3*y__1(t)-y__2(t)-4*y__3(t), diff(y__3(t),t) = y__1(t)-y__2(t)+9*y__3(t), y__1(0) = -4, y__2(0) = 1, y__3(0) = -3],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1}\relax (t ) = -\frac {50 \,{\mathrm e}^{7 t}}{11}+\frac {22 \,{\mathrm e}^{9 t}}{13}-\frac {164 \,{\mathrm e}^{-4 t}}{143} \] \[ y_{2}\relax (t ) = \frac {5 \,{\mathrm e}^{7 t}}{11}+\frac {22 \,{\mathrm e}^{9 t}}{13}-\frac {164 \,{\mathrm e}^{-4 t}}{143} \] \[ y_{3}\relax (t ) = -\frac {11 \,{\mathrm e}^{9 t}}{2}+\frac {5 \,{\mathrm e}^{7 t}}{2} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 57
DSolve[{y1'[t]==4*y1[t]-8*y2[t]-4*y3[t],y2'[t]==-3*y1[t]-1*y2[t]-3*y3[t],y3'[t]==1*y1[t]-1*y2[t]+9*y3[t]},{y1[0]==-4,y2[0]==1,y3[0]==-3},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{8 t} (8 t-3)-e^{-4 t} \\ \text {y2}(t)\to 2 e^{8 t}-e^{-4 t} \\ \text {y3}(t)\to -e^{8 t} (8 t+3) \\ \end{align*}