ODE
\[ -2 x^2 y'(x)+2 y'(x)^2+3 x y(x)=0 \] ODE Classification
[[_homogeneous, `class G`]]
Book solution method
Homogeneous ODE, The Isobaric equation
Mathematica ✗
cpu = 599.999 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.13 (sec), leaf count = 122
\[ \left \{ {1 \left ( \left ( -{\it \_C1}+y \left ( x \right ) \right ) \sqrt {{x}^{4}-6\,xy \left ( x \right ) }-{x}^{2} \left ( {\it \_C1}+y \left ( x \right ) \right ) \right ) \left ( {x}^{2}+\sqrt {{x}^{4}-6\,xy \left ( x \right ) } \right ) ^{-1}}=0,-{\frac {{x}^{2}}{y \left ( x \right ) } \left ( {x}^{2}+\sqrt {{x}^{4}-6\,xy \left ( x \right ) } \right ) ^{-1}}+{\frac {1}{y \left ( x \right ) }\sqrt {{x}^{4}-6\,xy \left ( x \right ) } \left ( {x}^{2}+\sqrt {{x}^{4}-6\,xy \left ( x \right ) } \right ) ^{-1}}-{\it \_C1}=0,y \left ( x \right ) ={\frac {{x}^{3}}{6}} \right \} \] Mathematica raw input
DSolve[3*x*y[x] - 2*x^2*y'[x] + 2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(2*diff(y(x),x)^2-2*x^2*diff(y(x),x)+3*x*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = 1/6*x^3, ((-_C1+y(x))*(x^4-6*x*y(x))^(1/2)-x^2*(_C1+y(x)))/(x^2+(x^4-6*x*y(x))^(1/2)) = 0, -1/y(x)/(x^2+(x^4-6*x*y(x))^(1/2))*x^2+1/y(x)/(x^2+(x^4-6*x*y(x))^(1/2))*(x^4-6*x*y(x))^(1/2)-_C1 = 0