60.1.348 problem 349

Internal problem ID [10362]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 349
Date solved : Monday, January 27, 2025 at 07:30:47 PM
CAS classification : [[_homogeneous, `class A`]]

\begin{align*} 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 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

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)
 

\[ y = \arcsin \left (\frac {1}{2 \ln \left (x \right )+2 c_{1}}\right ) x \]

✓ Solution by Mathematica

Time used: 0.482 (sec). Leaf size: 20

DSolve[2*x*Sin[y[x]/x] - Cot[y[x]/x]*y[x] + x*Cot[y[x]/x]*D[y[x],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*}