Internal problem ID [15007]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 5. Homogeneous equations. Exercises page 44
Problem number: 100.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y^{\prime } x -y-x \cos \left (\frac {y}{x}\right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 11
dsolve(x*diff(y(x),x)=y(x)+x*cos(y(x)/x)^2,y(x), singsol=all)
\[ y = \arctan \left (\ln \left (x \right )+c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.434 (sec). Leaf size: 35
DSolve[x*y'[x]==y[x]+x*Cos[y[x]/x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \tan ^{-1}(\log (x)+2 c_1) \\ y(x)\to -\frac {\pi x}{2} \\ y(x)\to \frac {\pi x}{2} \\ \end{align*}