Internal problem ID [2948]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 200.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x +x -y+x \cos \left (\frac {y}{x}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 12
dsolve(x*diff(y(x),x)+x-y(x)+x*cos(y(x)/x) = 0,y(x), singsol=all)
\[ y \relax (x ) = -2 \arctan \left (\ln \relax (x )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.414 (sec). Leaf size: 31
DSolve[x y'[x]+x -y[x]+x Cos[y[x]/x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 x \text {ArcTan}(-\log (x)+c_1) \\ y(x)\to -\pi x \\ y(x)\to \pi x \\ \end{align*}