Internal problem ID [1883]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\sin \relax (x ) \left (\cos ^{2}\relax (y)\right )+\left (\cos ^{2}\relax (x )\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 18
dsolve(sin(x)*cos(y(x))^2+cos(x)^2*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\arctan \left (\frac {\cos \relax (x ) c_{1}+1}{\cos \relax (x )}\right ) \]
✓ Solution by Mathematica
Time used: 1.588 (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 \text {ArcTan}(-\sec (x)+c_1) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}