Internal problem ID [1596]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 10 Linear system of Differential equations. Section 10.4, constant coefficient
homogeneous system. Page 540
Problem number: section 10.4, problem 8.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=y_{1}\relax (t )-y_{2}\relax (t )-2 y_{3}\relax (t )\\ y_{2}^{\prime }\relax (t )&=y_{1}\relax (t )-2 y_{2}\relax (t )-3 y_{3}\relax (t )\\ y_{3}^{\prime }\relax (t )&=-4 y_{1}\relax (t )+y_{2}\relax (t )-y_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.065 (sec). Leaf size: 73
dsolve([diff(y__1(t),t)=1*y__1(t)-1*y__2(t)-2*y__3(t),diff(y__2(t),t)=1*y__1(t)-2*y__2(t)-3*y__3(t),diff(y__3(t),t)=-4*y__1(t)+1*y__2(t)-1*y__3(t)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1}\relax (t ) = -c_{1} {\mathrm e}^{2 t}-c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{-3 t} \] \[ y_{2}\relax (t ) = -c_{1} {\mathrm e}^{2 t}-4 c_{2} {\mathrm e}^{-t}+2 c_{3} {\mathrm e}^{-3 t} \] \[ y_{3}\relax (t ) = c_{1} {\mathrm e}^{2 t}+c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 102
DSolve[{y1'[t]==1*y1[t]-1*y2[t]-2*y3[t],y2'[t]==1*y1[t]-2*y2[t]-3*y3[t],y1'[t]==-4*y1[t]+1*y2[t]-1*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to \frac {1}{576} e^{-3 t} \left (c_1 \left (63-128 e^t\right )+c_2 \left (64 e^t-27\right )\right ) \\ \text {y2}(t)\to \frac {1}{864} e^{-3 t} \left (c_2 \left (224 e^t-81\right )-7 c_1 \left (64 e^t-27\right )\right ) \\ \text {y3}(t)\to \frac {e^{-3 t} \left (c_1 \left (189-128 e^t\right )+c_2 \left (64 e^t-81\right )\right )}{1728} \\ \end{align*}