80.2.1 problem 4 (a)

Internal problem ID [18540]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 24. Problems at page 62
Problem number : 4 (a)
Date solved : Tuesday, January 28, 2025 at 11:54:45 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 11

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

\[ y \left (x \right ) = -\arctan \left (\sec \left (x \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 1.507 (sec). Leaf size: 31

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

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