4.19.10 $x^3+x^2{y}^{\prime }(x{)}^2-3xy(x)y^{\prime }(x)+2y(x{)}^2=0$

ODE
$$x^3+x^2{y}^{\prime }(x{)}^2-3xy(x)y^{\prime }(x)+2y(x{)}^2=0$$ 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

$$\{{\left(y\left(x\right)\right)}^2-4x^3=0,\frac{y\left(x\right)}{x^2}+\frac{1}{x^2}\sqrt{{\left(y\left(x\right)\right)}^2-4x^3}-\mathit{\_}\mathit{C}\mathit{1}=0,\frac{y\left(x\right)}{x}+\frac{1}{x}\sqrt{{\left(y\left(x\right)\right)}^2-4x^3}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$ 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