Internal problem ID [7937]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 357.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {x y^{\prime } \ln \relax (x ) \sin \relax (y)+\cos \relax (y) \left (1-x \cos \relax (y)\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 13
dsolve(x*diff(y(x),x)*ln(x)*sin(y(x))+cos(y(x))*(1-x*cos(y(x))) = 0,y(x), singsol=all)
\[ y \relax (x ) = \arccos \left (\frac {\ln \relax (x )}{x +c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 0.994 (sec). Leaf size: 53
DSolve[Cos[y[x]]*(1 - x*Cos[y[x]]) + x*Log[x]*Sin[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sec ^{-1}\left (\frac {x-c_1}{\log (x)}\right ) \\ y(x)\to \sec ^{-1}\left (\frac {x-c_1}{\log (x)}\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}