32.5.25 problem Exercise 11.27, page 97

Internal problem ID [5863]
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
Date solved : Monday, January 27, 2025 at 01:21:30 PM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=2 \tan \left (x \right ) \sec \left (x \right )-y^{2} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

dsolve(diff(y(x),x)=2*tan(x)*sec(x)-y(x)^2*sin(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-2 \cos \left (x \right )^{2} c_{1} +\sec \left (x \right )}{\cos \left (x \right )^{3} c_{1} +1} \]

✓ Solution by Mathematica

Time used: 0.805 (sec). Leaf size: 32

DSolve[D[y[x],x]==2*Tan[x]*Sec[x]-y[x]^2*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {\sec (x) \left (-2 \cos ^3(x)+c_1\right )}{\cos ^3(x)+c_1} \\ y(x)\to \sec (x) \\ \end{align*}