Internal problem ID [13142]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 40.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{2}-y^{2} \cos \left (x \right )+y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(y(x)^2-y(x)^2*cos(x)+diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{\sin \left (x \right )-c_{1} -x} \]
✓ Solution by Mathematica
Time used: 0.123 (sec). Leaf size: 22
DSolve[y[x]^2-y[x]^2*Cos[x]+y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{x-\sin (x)-c_1} y(x)\to 0 \end{align*}