78.4.16 problem 17

Internal problem ID [18139]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 8 (Exact Equations). Problems at page 72
Problem number : 17
Date solved : Tuesday, January 28, 2025 at 11:32:38 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: 0.007 (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 &= \sqrt {x +c_1}\, \sec \left (x \right ) \\ y &= -\sqrt {x +c_1}\, \sec \left (x \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.259 (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*}