Internal problem ID [14179]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (2-\frac {5}{y^{2}}\right ) y^{\prime }=-4 \cos \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 107
dsolve((2-5/y(x)^2)*diff(y(x),x)+4*cos(x)^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -c_{1} -\frac {x}{2}-\frac {\sin \left (2 x \right )}{4}-\frac {\sqrt {-158+16 \left (x +2 c_{1} \right ) \sin \left (2 x \right )+16 x^{2}+64 c_{1} x +64 c_{1}^{2}-2 \cos \left (4 x \right )}}{8} \\ y \left (x \right ) &= -c_{1} -\frac {x}{2}-\frac {\sin \left (2 x \right )}{4}+\frac {\sqrt {-158+16 \left (x +2 c_{1} \right ) \sin \left (2 x \right )+16 x^{2}+64 c_{1} x +64 c_{1}^{2}-2 \cos \left (4 x \right )}}{8} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.672 (sec). Leaf size: 88
DSolve[(2-5/y[x]^2)*y'[x]+4*Cos[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (-2 x-\sin (2 x)-\sqrt {-40+(2 x+\sin (2 x)-c_1){}^2}+c_1\right ) \\ y(x)\to \frac {1}{4} \left (-2 x-\sin (2 x)+\sqrt {-40+(2 x+\sin (2 x)-c_1){}^2}+c_1\right ) \\ y(x)\to 0 \\ \end{align*}