Internal problem ID [10116]
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]
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: 0.0 (sec). Leaf size: 18
dsolve(sin(x)*cos(y(x))^2+cos(x)^2*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\arctan \left (\frac {c_{1} \cos \relax (x )+1}{\cos \relax (x )}\right ) \]
✓ Solution by Mathematica
Time used: 1.685 (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*}