Internal problem ID [1621]
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 18.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=-y_{1}\relax (t )+y_{2}\relax (t )\\ y_{2}^{\prime }\relax (t )&=y_{1}\relax (t )-y_{2}\relax (t )-2 y_{3}\relax (t )\\ y_{3}^{\prime }\relax (t )&=-y_{1}\relax (t )-y_{2}\relax (t )-y_{3}\relax (t ) \end {align*}
With initial conditions \[ [y_{1}\relax (0) = 6, y_{2}\relax (0) = 5, y_{3}\relax (0) = -7] \]
✓ Solution by Maple
Time used: 0.066 (sec). Leaf size: 57
dsolve([diff(y__1(t),t) = -y__1(t)+y__2(t), diff(y__2(t),t) = y__1(t)-y__2(t)-2*y__3(t), diff(y__3(t),t) = -y__1(t)-y__2(t)-y__3(t), y__1(0) = 6, y__2(0) = 5, y__3(0) = -7],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1}\relax (t ) = 4 \,{\mathrm e}^{t}+2 \,{\mathrm e}^{-2 t}-t \,{\mathrm e}^{-2 t} \] \[ y_{2}\relax (t ) = t \,{\mathrm e}^{-2 t}+8 \,{\mathrm e}^{t}-3 \,{\mathrm e}^{-2 t} \] \[ y_{3}\relax (t ) = -6 \,{\mathrm e}^{t}-{\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 55
DSolve[{y1'[t]==-1*y1[t]+1*y2[t]+0*y3[t],y2'[t]==1*y1[t]-1*y2[t]-2*y3[t],y3'[t]==-1*y1[t]-1*y2[t]-1*y3[t]},{y1[0]==6,y2[0]==5,y3[0]==-7},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to 4 e^t-e^{-2 t} (t-2) \\ \text {y2}(t)\to e^{-2 t} (t-3)+8 e^t \\ \text {y3}(t)\to -e^{-2 t}-6 e^t \\ \end{align*}