78.4.2 problem 2

Internal problem ID [18125]
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 : 2
Date solved : Tuesday, January 28, 2025 at 11:29:24 AM
CAS classification : [`y=_G(x,y')`]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 1.640 (sec). Leaf size: 54

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

\begin{align*} y(x)\to -\arctan (\sin (x)+c_1 \cos (x)) \\ y(x)\to -\frac {1}{2} \pi \sqrt {\cos ^2(x)} \sec (x) \\ y(x)\to \frac {1}{2} \pi \sqrt {\cos ^2(x)} \sec (x) \\ \end{align*}