4.21.40 $y^{\prime }(x{)}^3-2y(x)y^{\prime }(x)+y(x{)}^2=0$

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

[_quadrature]

Book solution method
Missing Variables ODE, Independent variable missing, Solve for $y$

Mathematica ✗
cpu = 0 (sec), leaf count = 0 , crash

Kernel Crash

Maple ✓
cpu = 0.052 (sec), leaf count = 259

$$\{x-{\int }^{y\left(x\right)}6\frac{\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{a}}^4-32{\mathit{\_}\mathit{a}}^3}}}{{(-108{\mathit{\_}\mathit{a}}^2+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{a}}^4-32{\mathit{\_}\mathit{a}}^3})}^{2/3}+24\mathit{\_}\mathit{a}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\int }^{y\left(x\right)}12\frac{\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{a}}^4-32{\mathit{\_}\mathit{a}}^3}}}{(i\sqrt{3}-1)(12i\mathit{\_}\mathit{a}\sqrt{3}+{(-108{\mathit{\_}\mathit{a}}^2+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{a}}^4-32{\mathit{\_}\mathit{a}}^3})}^{2/3}-12\mathit{\_}\mathit{a})}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\int }^{y\left(x\right)}12\frac{\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{a}}^4-32{\mathit{\_}\mathit{a}}^3}}}{(i\sqrt{3}+1)(12i\mathit{\_}\mathit{a}\sqrt{3}-{(-108{\mathit{\_}\mathit{a}}^2+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{a}}^4-32{\mathit{\_}\mathit{a}}^3})}^{2/3}+12\mathit{\_}\mathit{a})}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

DSolve[y[x]^2 - 2*y[x]*y'[x] + y'[x]^3 == 0,y[x],x]

Mathematica raw output

""

Maple raw input

dsolve(diff(y(x),x)^3-2*y(x)*diff(y(x),x)+y(x)^2 = 0, y(x),'implicit')

Maple raw output

x-Intat(6/((-108*_a^2+12*3^(1/2)*(27*_a^4-32*_a^3)^(1/2))^(2/3)+24*_a)*(-108*_a^
2+12*3^(1/2)*(27*_a^4-32*_a^3)^(1/2))^(1/3),_a = y(x))-_C1 = 0, x-Intat(12/(I*3^
(1/2)+1)/(12*I*_a*3^(1/2)-(-108*_a^2+12*3^(1/2)*(27*_a^4-32*_a^3)^(1/2))^(2/3)+1
2*_a)*(-108*_a^2+12*3^(1/2)*(27*_a^4-32*_a^3)^(1/2))^(1/3),_a = y(x))-_C1 = 0, x
-Intat(12/(I*3^(1/2)-1)/(12*I*_a*3^(1/2)+(-108*_a^2+12*3^(1/2)*(27*_a^4-32*_a^3)
^(1/2))^(2/3)-12*_a)*(-108*_a^2+12*3^(1/2)*(27*_a^4-32*_a^3)^(1/2))^(1/3),_a = y
(x))-_C1 = 0