Internal problem ID [6725]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS.
EXERCISES 8.1. Page 332
Problem number: 15.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )+2 y \left (t \right )+z \left (t \right )\\ y^{\prime }\left (t \right )&=6 x \left (t \right )-y \left (t \right )\\ z^{\prime }\left (t \right )&=-x \left (t \right )-2 y \left (t \right )-z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 61
dsolve([diff(x(t),t)=x(t)+2*y(t)+z(t),diff(y(t),t)=6*x(t)-y(t),diff(z(t),t)=-x(t)-2*y(t)-z(t)],[x(t), y(t), z(t)], singsol=all)
\[ x \left (t \right ) = -c_{2} {\mathrm e}^{-4 t}-c_{3} {\mathrm e}^{3 t}-\frac {c_{1}}{13} \] \[ y \left (t \right ) = 2 c_{2} {\mathrm e}^{-4 t}-\frac {3 c_{3} {\mathrm e}^{3 t}}{2}-\frac {6 c_{1}}{13} \] \[ z \left (t \right ) = c_{1} +c_{2} {\mathrm e}^{-4 t}+c_{3} {\mathrm e}^{3 t} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 190
DSolve[{x'[t]==x[t]+2*y[t]+z[t],y'[t]==6*x[t]-y[t],z'[t]==-x[t]-2*y[t]-z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{84} e^{-4 t} \left (c_1 \left (-7 e^{4 t}+64 e^{7 t}+27\right )+24 c_2 \left (e^{7 t}-1\right )+c_3 \left (-7 e^{4 t}+16 e^{7 t}-9\right )\right ) y(t)\to \frac {1}{14} e^{-4 t} \left (c_1 \left (-7 e^{4 t}+16 e^{7 t}-9\right )+c_2 \left (6 e^{7 t}+8\right )+c_3 \left (-7 e^{4 t}+4 e^{7 t}+3\right )\right ) z(t)\to \frac {1}{84} e^{-4 t} \left (c_1 \left (91 e^{4 t}-64 e^{7 t}-27\right )-24 c_2 \left (e^{7 t}-1\right )-c_3 \left (-91 e^{4 t}+16 e^{7 t}-9\right )\right ) \end{align*}