Internal problem ID [7704]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 124.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {x y^{\prime }+x \cos \left (\frac {y}{x}\right )-y+x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 12
dsolve(x*diff(y(x),x) + x*cos(y(x)/x) - 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: 0.424 (sec). Leaf size: 31
DSolve[x*y'[x] + x*Cos[y[x]/x] - y[x] + x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 x \operatorname {ArcTan}(-\log (x)+c_1) \\ y(x)\to -\pi x \\ y(x)\to \pi x \\ \end{align*}