Internal problem ID [5996]
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 8.2. Page 346
Problem number: 24.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=3 x \relax (t )+2 y \relax (t )+4 z \relax (t )\\ y^{\prime }\relax (t )&=2 x \relax (t )+2 z \relax (t )\\ z^{\prime }\relax (t )&=4 x \relax (t )+2 y \relax (t )+3 z \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 66
dsolve([diff(x(t),t)=3*x(t)+2*y(t)+4*z(t),diff(y(t),t)=2*x(t)+2*z(t),diff(z(t),t)=4*x(t)+2*y(t)+3*z(t)],[x(t), y(t), z(t)], singsol=all)
\[ x \relax (t ) = -\frac {5 c_{2} {\mathrm e}^{-t}}{4}+c_{3} {\mathrm e}^{8 t}-\frac {{\mathrm e}^{-t} c_{1}}{2} \] \[ y \relax (t ) = \frac {c_{2} {\mathrm e}^{-t}}{2}+\frac {c_{3} {\mathrm e}^{8 t}}{2}+{\mathrm e}^{-t} c_{1} \] \[ z \relax (t ) = c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{8 t} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 127
DSolve[{x'[t]==3*x[t]+2*y[t]+4*z[t],y'[t]==2*x[t]+2*z[t],z'[t]==4*x[t]+2*y[t]+3*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{9} e^{-t} \left (c_1 \left (4 e^{9 t}+5\right )+2 (c_2+2 c_3) \left (e^{9 t}-1\right )\right ) \\ y(t)\to \frac {1}{9} e^{-t} \left ((2 c_1+c_2+2 c_3) e^{9 t}-2 (c_1-4 c_2+c_3)\right ) \\ z(t)\to \frac {1}{9} e^{-t} \left (2 (2 c_1+c_2+2 c_3) e^{9 t}-4 c_1-2 c_2+5 c_3\right ) \\ \end{align*}