Internal problem ID [11140]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 2.833 (sec). Leaf size: 31
DSolve[Sin[x]*Cos[y[x]]^2+Cos[x]^2*y'[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*}