Internal problem ID [14404]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Review exercises, page 80
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {-8 \sin \left (y\right ) y^{\prime }=-\cos \left (4 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(cos(4*x)-8*sin(y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\pi }{2}+\arcsin \left (\frac {\sin \left (4 x \right )}{32}+\frac {c_{1}}{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.724 (sec). Leaf size: 39
DSolve[Cos[4*x]-8*Sin[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\arccos \left (-\frac {1}{32} \sin (4 x)-c_1\right ) \\ y(x)\to \arccos \left (-\frac {1}{32} \sin (4 x)-c_1\right ) \\ \end{align*}