Internal problem ID [6009]
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 }\relax (t )&=z \relax (t )\\ y^{\prime }\relax (t )&=-z \relax (t )\\ z^{\prime }\relax (t )&=y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.171 (sec). Leaf size: 41
dsolve([diff(x(t),t)=z(t),diff(y(t),t)=-z(t),diff(z(t),t)=y(t)],[x(t), y(t), z(t)], singsol=all)
\[ x \relax (t ) = c_{3} \sin \relax (t )-\cos \relax (t ) c_{2}+c_{1} \] \[ y \relax (t ) = \cos \relax (t ) c_{2}-c_{3} \sin \relax (t ) \] \[ z \relax (t ) = c_{2} \sin \relax (t )+c_{3} \cos \relax (t ) \]
✓ Solution by Mathematica
Time used: 0.009 (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*}