Internal problem ID [6734]
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 }\left (t \right )&=2 x \left (t \right )-7 y\\ y^{\prime }&=5 x \left (t \right )+10 y+4 z \left (t \right )\\ z^{\prime }\left (t \right )&=5 y+2 z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)],singsol=all)
\begin{align*} x \left (t \right ) &= -\frac {7 c_{3} {\mathrm e}^{7 t}}{5}-\frac {7 c_{2} {\mathrm e}^{5 t}}{3}+c_{1} {\mathrm e}^{2 t} \\ y \left (t \right ) &= c_{2} {\mathrm e}^{5 t}+c_{3} {\mathrm e}^{7 t} \\ z \left (t \right ) &= \frac {5 c_{2} {\mathrm e}^{5 t}}{3}+c_{3} {\mathrm e}^{7 t}-\frac {5 c_{1} {\mathrm e}^{2 t}}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 190
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} e^{2 t} \left (5 c_1 \left (-35 e^{3 t}+21 e^{5 t}+8\right )+7 \left (-5 (3 c_2+4 c_3) e^{3 t}+3 (5 c_2+4 c_3) e^{5 t}+8 c_3\right )\right ) \\ y(t)\to \frac {1}{2} e^{5 t} \left (5 c_1 \left (e^{2 t}-1\right )+c_2 \left (5 e^{2 t}-3\right )+4 c_3 \left (e^{2 t}-1\right )\right ) \\ z(t)\to \frac {1}{6} e^{2 t} \left (5 c_1 \left (-5 e^{3 t}+3 e^{5 t}+2\right )-5 (3 c_2+4 c_3) e^{3 t}+3 (5 c_2+4 c_3) e^{5 t}+14 c_3\right ) \\ \end{align*}