Internal problem ID [5997]
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: 25.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=5 x \relax (t )-4 y \relax (t )\\ y^{\prime }\relax (t )&=x \relax (t )+2 z \relax (t )\\ z^{\prime }\relax (t )&=2 y \relax (t )+5 z \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 63
dsolve([diff(x(t),t)=5*x(t)-4*y(t),diff(y(t),t)=x(t)+2*z(t),diff(z(t),t)=2*y(t)+5*z(t)],[x(t), y(t), z(t)], singsol=all)
\[ x \relax (t ) = -2 c_{2} {\mathrm e}^{5 t}-2 c_{3} {\mathrm e}^{5 t} t +\frac {5 c_{3} {\mathrm e}^{5 t}}{2}-2 c_{1} \] \[ y \relax (t ) = \frac {c_{3} {\mathrm e}^{5 t}}{2}-\frac {5 c_{1}}{2} \] \[ z \relax (t ) = c_{1}+c_{2} {\mathrm e}^{5 t}+c_{3} {\mathrm e}^{5 t} t \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 132
DSolve[{x'[t]==5*x[t]-4*y[t],y'[t]==x[t]+2*z[t],z'[t]==2*y[t]+5*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{25} \left (e^{5 t} (c_1 (29-20 t)+8 c_3 (1-5 t)-20 c_2)-4 (c_1-5 c_2+2 c_3)\right ) \\ y(t)\to \frac {1}{5} c_1 \left (e^{5 t}-1\right )+\frac {2}{5} c_3 \left (e^{5 t}-1\right )+c_2 \\ z(t)\to \frac {1}{25} \left (e^{5 t} (2 c_1 (5 t-1)+c_3 (20 t+21)+10 c_2)+2 (c_1-5 c_2+2 c_3)\right ) \\ \end{align*}