Internal problem ID [6762]
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: 39.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=z \left (t \right )\\ y^{\prime }&=-z \left (t \right )\\ z^{\prime }\left (t \right )&=y \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 41
dsolve([diff(x(t),t)=z(t),diff(y(t),t)=-z(t),diff(z(t),t)=y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{3} \sin \left (t \right )-c_{2} \cos \left (t \right )+c_{1} \\ y \left (t \right ) &= -c_{3} \sin \left (t \right )+c_{2} \cos \left (t \right ) \\ z \left (t \right ) &= c_{2} \sin \left (t \right )+c_{3} \cos \left (t \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 50
DSolve[{x'[t]==z[t],y'[t]==-z[t],z'[t]==y[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -c_2 \cos (t)+c_3 \sin (t)+c_1+c_2 \\ y(t)\to c_2 \cos (t)-c_3 \sin (t) \\ z(t)\to c_3 \cos (t)+c_2 \sin (t) \\ \end{align*}