Internal problem ID [3456]
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]
\[ \boxed {x y^{\prime }-y+x \cos \left (\frac {y}{x}\right )=-x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve(x*diff(y(x),x)+x-y(x)+x*cos(y(x)/x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = -2 \arctan \left (\ln \left (x \right )+c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.435 (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 \arctan (-\log (x)+c_1) y(x)\to -\pi x y(x)\to \pi x \end{align*}