Internal problem ID [5981]
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: 8.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=2 x \relax (t )-7 y \relax (t )\\ y^{\prime }\relax (t )&=5 x \relax (t )+10 y \relax (t )+4 z \relax (t )\\ z^{\prime }\relax (t )&=5 y \relax (t )+2 z \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.101 (sec). Leaf size: 66
dsolve([diff(x(t),t)=2*x(t)-7*y(t),diff(y(t),t)=5*x(t)+10*y(t)+4*z(t),diff(z(t),t)=5*y(t)+2*z(t)],[x(t), y(t), z(t)], singsol=all)
\[ x \relax (t ) = -\frac {4 c_{1} {\mathrm e}^{2 t}}{5}-\frac {7 c_{2} {\mathrm e}^{5 t}}{5}-\frac {7 c_{3} {\mathrm e}^{7 t}}{5} \] \[ y \relax (t ) = \frac {3 c_{2} {\mathrm e}^{5 t}}{5}+c_{3} {\mathrm e}^{7 t} \] \[ z \relax (t ) = c_{1} {\mathrm e}^{2 t}+c_{2} {\mathrm e}^{5 t}+c_{3} {\mathrm e}^{7 t} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 158
DSolve[{x'[t]==2*x[t]-7*y[t],y'[t]==5*x[t]+10*y[t]+4*z[t],z'[t]==5*y[t]+2*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{30} \left (35 (5 c_1+3 c_2+4 c_3) e^{5 t}-21 (5 (c_1+c_2)+4 c_3) e^{7 t}-8 (5 c_1+7 c_3) e^{2 t}\right ) \\ y(t)\to e^{6 t} (c_2 \cosh (t)+(5 c_1+4 (c_2+c_3)) \sinh (t)) \\ z(t)\to \frac {1}{6} \left (-5 (5 c_1+3 c_2+4 c_3) e^{5 t}+3 (5 (c_1+c_2)+4 c_3) e^{7 t}+2 (5 c_1+7 c_3) e^{2 t}\right ) \\ \end{align*}