Internal problem ID [12112]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\tan \left (y\right )-y^{\prime } \cot \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 9
dsolve(tan(y(x))-cot(x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \arcsin \left (\sec \left (x \right ) c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 4.745 (sec). Leaf size: 19
DSolve[Tan[y[x]]-Cot[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \arcsin \left (\frac {1}{2} c_1 \sec (x)\right ) \\ y(x)\to 0 \\ \end{align*}