32.5.22 problem Exercise 11.23, page 97

Internal problem ID [5860]
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 11.23, page 97
Date solved : Monday, January 27, 2025 at 01:21:08 PM
CAS classification : [_Bernoulli]

\begin{align*} 2 \cos \left (x \right ) y^{\prime }&=y \sin \left (x \right )-y^{3} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.614 (sec). Leaf size: 33

dsolve([2*cos(x)*diff(y(x),x)=y(x)*sin(x)-y(x)^3,y(0) = 1],y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\sqrt {\left (2 \cos \left (x \right )^{2}-1\right ) \left (-\sin \left (x \right )+\cos \left (x \right )\right )}}{2 \cos \left (x \right )^{2}-1} \]

✓ Solution by Mathematica

Time used: 0.391 (sec). Leaf size: 14

DSolve[{2*Cos[x]*D[y[x],x]==y[x]*Sin[x]-y[x]^3,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{\sqrt {\sin (x)+\cos (x)}} \]