Internal problem ID [5986]
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: 12.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=-x \relax (t )+4 y \relax (t )+2 z \relax (t )\\ y^{\prime }\relax (t )&=4 x \relax (t )-y \relax (t )-2 z \relax (t )\\ z^{\prime }\relax (t )&=6 z \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 58
dsolve([diff(x(t),t)=-x(t)+4*y(t)+2*z(t),diff(y(t),t)=4*x(t)-y(t)-2*z(t),diff(z(t),t)=6*z(t)],[x(t), y(t), z(t)], singsol=all)
\[ x \relax (t ) = \frac {2 c_{3} {\mathrm e}^{6 t}}{11}-{\mathrm e}^{-5 t} c_{1}+{\mathrm e}^{3 t} c_{2} \] \[ y \relax (t ) = {\mathrm e}^{3 t} c_{2}+{\mathrm e}^{-5 t} c_{1}-\frac {2 c_{3} {\mathrm e}^{6 t}}{11} \] \[ z \relax (t ) = c_{3} {\mathrm e}^{6 t} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 105
DSolve[{x'[t]==-x[t]+4*y[t]+2*z[t],y'[t]==4*x[t]-y[t]-2*z[t],z'[t]==6*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{22} e^{-5 t} \left (11 c_1 \left (e^{8 t}+1\right )+11 c_2 \left (e^{8 t}-1\right )+4 c_3 \left (e^{11 t}-1\right )\right ) \\ y(t)\to \frac {1}{22} e^{-5 t} \left (11 c_1 \left (e^{8 t}-1\right )+11 c_2 \left (e^{8 t}+1\right )-4 c_3 \left (e^{11 t}-1\right )\right ) \\ z(t)\to c_3 e^{6 t} \\ \end{align*}