Internal problem ID [7928]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 349.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`]]
\[ \boxed {x y^{\prime } \cot \left (\frac {y}{x}\right )+2 x \sin \left (\frac {y}{x}\right )-y \cot \left (\frac {y}{x}\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(x*diff(y(x),x)*cot(y(x)/x)+2*x*sin(y(x)/x)-y(x)*cot(y(x)/x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = \arcsin \left (\frac {1}{2 c_{1} +2 \ln \left (x \right )}\right ) x \]
✓ Solution by Mathematica
Time used: 0.491 (sec). Leaf size: 20
DSolve[2*x*Sin[y[x]/x] - Cot[y[x]/x]*y[x] + x*Cot[y[x]/x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \csc ^{-1}(2 (\log (x)+c_1)) \\ y(x)\to 0 \\ \end{align*}