Internal problem ID [12149]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 71.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y-y^{\prime } \cos \left (x \right )-y^{2} \cos \left (x \right ) \left (-\sin \left (x \right )+1\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(y(x)-diff(y(x),x)*cos(x)=y(x)^2*cos(x)*(1-sin(x)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sec \left (x \right )+\tan \left (x \right )}{\sin \left (x \right )+c_{1}} \]
✓ Solution by Mathematica
Time used: 0.778 (sec). Leaf size: 41
DSolve[y[x]-y'[x]*Cos[x]==y[x]^2*Cos[x]*(1-Sin[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{2 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )}}{\cos (x) e^{2 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )}+c_1} y(x)\to 0 \end{align*}