ODE
\[ x^3+x^2 y'(x)^2-3 x y(x) y'(x)+2 y(x)^2=0 \] ODE Classification
[[_homogeneous, `class G`], _rational]
Book solution method
Change of variable
Mathematica ✗
cpu = 600.014 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.105 (sec), leaf count = 69
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{2}-4\,{x}^{3}=0,{\frac {y \left ( x \right ) }{{x}^{2}}}+{\frac {1}{{x}^{2}}\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-4\,{x}^{3}}}-{\it \_C1}=0,{\frac {y \left ( x \right ) }{x}}+{\frac {1}{x}\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-4\,{x}^{3}}}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[x^3 + 2*y[x]^2 - 3*x*y[x]*y'[x] + x^2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(x^2*diff(y(x),x)^2-3*x*y(x)*diff(y(x),x)+x^3+2*y(x)^2 = 0, y(x),'implicit')
Maple raw output
y(x)^2-4*x^3 = 0, y(x)/x+1/x*(y(x)^2-4*x^3)^(1/2)-_C1 = 0, 1/x^2*y(x)+1/x^2*(y(x)^2-4*x^3)^(1/2)-_C1 = 0