62.2.4 problem Ex 4

Internal problem ID [12806]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 9. Variables searated or separable. Page 13
Problem number : Ex 4
Date solved : Tuesday, January 28, 2025 at 04:22:04 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)
 

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

✓ Solution by Mathematica

Time used: 1.565 (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*}