Internal problem ID [4010]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli
Equations
Problem number: Exercise 11.27, page 97.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-2 \sec \left (x \right ) \tan \left (x \right )+\sin \left (x \right ) y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve(diff(y(x),x)=2*tan(x)*sec(x)-y(x)^2*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sec \left (x \right ) \tan \left (x \right )}{\sin \left (x \right ) \left (c_{1} \cos \left (x \right )^{2}+\sec \left (x \right )\right )}-\frac {2 c_{1} \cos \left (x \right )}{c_{1} \cos \left (x \right )^{2}+\sec \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.534 (sec). Leaf size: 29
DSolve[y'[x]==2*Tan[x]*Sec[x]-y[x]^2*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sec (x)-\frac {3 \cos ^2(x)}{\cos ^3(x)+c_1} \\ y(x)\to \sec (x) \\ \end{align*}