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