4.19.10 \(x^3+x^2 y'(x)^2-3 x y(x) y'(x)+2 y(x)^2=0\)

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

\[ \left \{ \left (y \relax (x ) \right ) ^{2}-4\,{x}^{3}=0,{\frac {y \relax (x ) }{{x}^{2}}}+{\frac {1}{{x}^{2}}\sqrt { \left (y \relax (x ) \right ) ^{2}-4\,{x}^{3}}}-{\it \_C1}=0,{\frac {y \relax (x ) }{x}}+{\frac {1}{x}\sqrt { \left (y \relax (x ) \right ) ^{2}-4\,{x}^{3}}}-{\it \_C1}=0 \right \} \] 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