Internal problem ID [2959]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 211.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x -y+\tan \left (\frac {y}{x}\right ) x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 14
dsolve(x*diff(y(x),x) = y(x)-x*tan(y(x)/x),y(x), singsol=all)
\[ y \relax (x ) = x \arcsin \left (\frac {1}{x c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 2.126 (sec). Leaf size: 21
DSolve[x y'[x]==y[x]-x Tan[y[x]/x],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*}