Internal problem ID [2953]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 205.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x -y+\sec \left (\frac {y}{x}\right ) x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 12
dsolve(x*diff(y(x),x)-y(x)+x*sec(y(x)/x) = 0,y(x), singsol=all)
\[ y \relax (x ) = -\arcsin \left (\ln \relax (x )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.314 (sec). Leaf size: 15
DSolve[x y'[x]-y[x]+x Sec[y[x]/x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \text {ArcSin}(-\log (x)+c_1) \\ \end{align*}