4.11.18 \(x^2 \cot ^{-1}\left (\frac {y(x)}{x}\right )+x y(x) y'(x)-y(x)^2=0\)

ODE
\[ x^2 \cot ^{-1}\left (\frac {y(x)}{x}\right )+x y(x) y'(x)-y(x)^2=0 \] ODE Classification

[[_homogeneous, `class A`], _dAlembert]

Book solution method
Homogeneous equation

Mathematica
cpu = 599.993 (sec), leaf count = 0 , timed out

$Aborted

Maple
cpu = 0.302 (sec), leaf count = 24

\[ \left \{ -{\it \_C1}+\int ^{{\frac {y \relax (x ) }{x}}}\!{\frac {{\it \_a}}{{\rm arccot} \left ({\it \_a}\right )}}{d{\it \_a}}+\ln \relax (x ) =0 \right \} \] Mathematica raw input

DSolve[x^2*ArcCot[y[x]/x] - y[x]^2 + x*y[x]*y'[x] == 0,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve(x*y(x)*diff(y(x),x)+x^2*arccot(y(x)/x)-y(x)^2 = 0, y(x),'implicit')

Maple raw output

-_C1+Intat(1/arccot(_a)*_a,_a = y(x)/x)+ln(x) = 0