Internal problem ID [7705]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 125.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {x y^{\prime }+x \tan \left (\frac {y}{x}\right )-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve(x*diff(y(x),x) + x*tan(y(x)/x) - y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = x \arcsin \left (\frac {1}{c_{1} x}\right ) \]
✓ Solution by Mathematica
Time used: 15.962 (sec). Leaf size: 21
DSolve[x*y'[x] + x*Tan[y[x]/x] - y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \text {ArcSin}\left (\frac {e^{c_1}}{x}\right ) \\ y(x)\to 0 \\ \end{align*}