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]
Solve \begin {gather*} \boxed {\tan \relax (x ) \left (\sin ^{2}\relax (x )\right )+\left (\cos ^{2}\relax (x )\right ) \cot \relax (y) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 1.163 (sec). Leaf size: 38
dsolve(tan(x)*sin(x)^2+cos(x)^2*cot(y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \arcsin \left (\frac {{\mathrm e}^{\frac {-2 \cos \left (2 x \right ) c_{1}+\cos \left (2 x \right )-2 c_{1}-1}{2 \cos \left (2 x \right )+2}}}{\cos \relax (x )}\right ) \]
✓ Solution by Mathematica
Time used: 11.451 (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 \text {ArcSin}\left (\frac {1}{8} c_1 e^{-\frac {1}{2} \sec ^2(x)} \sec (x)\right ) \\ \end{align*}