Internal problem ID [1622]
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 19.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=-2 y_{1}\relax (t )+2 y_{2}\relax (t )+y_{3}\relax (t )\\ y_{2}^{\prime }\relax (t )&=-2 y_{1}\relax (t )+2 y_{2}\relax (t )+y_{3}\relax (t )\\ y_{3}^{\prime }\relax (t )&=-3 y_{1}\relax (t )+3 y_{2}\relax (t )+2 y_{3}\relax (t ) \end {align*}
With initial conditions \[ [y_{1}\relax (0) = -6, y_{2}\relax (0) = -2, y_{3}\relax (0) = 0] \]
✓ Solution by Maple
Time used: 0.069 (sec). Leaf size: 41
dsolve([diff(y__1(t),t) = -2*y__1(t)+2*y__2(t)+y__3(t), diff(y__2(t),t) = -2*y__1(t)+2*y__2(t)+y__3(t), diff(y__3(t),t) = -3*y__1(t)+3*y__2(t)+2*y__3(t), y__1(0) = -6, y__2(0) = -2, y__3(0) = 0],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1}\relax (t ) = 3 \,{\mathrm e}^{2 t}+2 t -9 \] \[ y_{2}\relax (t ) = 3 \,{\mathrm e}^{2 t}+2 t -5 \] \[ y_{3}\relax (t ) = -6+6 \,{\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 44
DSolve[{y1'[t]==-2*y1[t]+2*y2[t]+1*y3[t],y2'[t]==-2*y1[t]+2*y2[t]+1*y3[t],y3'[t]==-3*y1[t]+3*y2[t]+2*y3[t]},{y1[0]==-6,y2[0]==-2,y3[0]==0},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to 2 t+3 e^{2 t}-9 \\ \text {y2}(t)\to 2 t+3 e^{2 t}-5 \\ \text {y3}(t)\to 6 \left (e^{2 t}-1\right ) \\ \end{align*}