Internal problem ID [1888]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\tan \left (x \right ) \sin \left (x \right )^{2}+\cos \left (x \right )^{2} \cot \left (y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 40
dsolve(tan(x)*sin(x)^2+cos(x)^2*cot(y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \arcsin \left (\frac {\sqrt {2}\, \sqrt {\frac {1}{1+\cos \left (2 x \right )}}\, {\mathrm e}^{\frac {-1+\cos \left (2 x \right )}{2 \cos \left (2 x \right )+2}}}{c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 16.527 (sec). Leaf size: 24
DSolve[Tan[x]*Sin[x]^2+Cos[x]^2*Cot[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \arcsin \left (\frac {1}{8} c_1 e^{-\frac {1}{2} \sec ^2(x)} \sec (x)\right ) \\ \end{align*}