Internal problem ID [7933]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 353.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\sin \relax (y)+y^{\prime } \cos \relax (y) x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 12
dsolve(x*diff(y(x),x)*cos(y(x))+sin(y(x)) = 0,y(x), singsol=all)
\[ y \relax (x ) = \arcsin \left (\frac {1}{c_{1} x}\right ) \]
✓ Solution by Mathematica
Time used: 2.476 (sec). Leaf size: 19
DSolve[Sin[y[x]] + x*Cos[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ArcSin}\left (\frac {e^{c_1}}{x}\right ) \\ y(x)\to 0 \\ \end{align*}