Internal problem ID [5972]
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 }\relax (t )&=x \relax (t )+2 y \relax (t )+z \relax (t )\\ y^{\prime }\relax (t )&=6 x \relax (t )-y \relax (t )\\ z^{\prime }\relax (t )&=-x \relax (t )-2 y \relax (t )-z \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.104 (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)
\[ x \relax (t ) = -c_{2} {\mathrm e}^{-4 t}-c_{3} {\mathrm e}^{3 t}-\frac {c_{1}}{13} \] \[ y \relax (t ) = 2 c_{2} {\mathrm e}^{-4 t}-\frac {3 c_{3} {\mathrm e}^{3 t}}{2}-\frac {6 c_{1}}{13} \] \[ z \relax (t ) = c_{1}+c_{2} {\mathrm e}^{-4 t}+c_{3} {\mathrm e}^{3 t} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 176
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 (-7 (c_1+c_3) e^{4 t}+8 (8 c_1+3 c_2+2 c_3) e^{7 t}+3 (9 c_1-8 c_2-3 c_3)\right ) \\ y(t)\to \frac {1}{14} e^{-4 t} \left (-7 (c_1+c_3) e^{4 t}+2 (8 c_1+3 c_2+2 c_3) e^{7 t}-9 c_1+8 c_2+3 c_3\right ) \\ z(t)\to \frac {1}{84} e^{-4 t} \left (91 (c_1+c_3) e^{4 t}-8 (8 c_1+3 c_2+2 c_3) e^{7 t}-27 c_1+24 c_2+9 c_3\right ) \\ \end{align*}