ODE
\[ -6 x^3 y'(x)+4 x^2 y(x)+y(x)^2 y'(x)^2=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries]]
Book solution method
Change of variable
Mathematica ✗
cpu = 599.998 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 3.643 (sec), leaf count = 62
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{3}-{\frac {9\,{x}^{4}}{4}}=0,\ln \left ( x \right ) -\int ^{{y \left ( x \right ) {x}^{-{\frac {4}{3}}}}}\!{\frac {1}{16\,{{\it \_a}}^{4}-36\,{\it \_a}} \left ( -12\,{{\it \_a}}^{3}-9\,\sqrt {-4\,{{\it \_a}}^{3}+9}+27 \right ) }{d{\it \_a}}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[4*x^2*y[x] - 6*x^3*y'[x] + y[x]^2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(y(x)^2*diff(y(x),x)^2-6*x^3*diff(y(x),x)+4*x^2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x)^3-9/4*x^4 = 0, ln(x)-Intat((-12*_a^3-9*(-4*_a^3+9)^(1/2)+27)/(16*_a^4-36*_a),_a = y(x)/x^(4/3))-_C1 = 0