28.1.94 problem 116

Internal problem ID [4400]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 116
Date solved : Monday, January 27, 2025 at 09:14:30 AM
CAS classification : [_exact, _Bernoulli]

\begin{align*} 1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 24

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

\begin{align*} y \left (x \right ) &= \sec \left (x \right ) \sqrt {x +c_{1}} \\ y \left (x \right ) &= -\sec \left (x \right ) \sqrt {x +c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.281 (sec). Leaf size: 32

DSolve[(1+y[x]^2*Sin[2*x])-(2*y[x]*Cos[x]^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {x+c_1} \sec (x) \\ y(x)\to \sqrt {x+c_1} \sec (x) \\ \end{align*}