Internal problem ID [2076]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.8, page 68
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x -\tan \left (\frac {y}{x}\right ) x -y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 10
dsolve(x*diff(y(x),x)=x*tan(y(x)/x)+y(x),y(x), singsol=all)
\[ y \relax (x ) = \arcsin \left (x c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 7.829 (sec). Leaf size: 19
DSolve[x*y'[x]==x*Tan[y[x]/x]+y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \text {ArcSin}\left (e^{c_1} x\right ) \\ y(x)\to 0 \\ \end{align*}