ODE
\[ -x^3 y(x)^3+x \left (x^2+x y(x)+y(x)^2\right ) y(x) y'(x)-\left (x^2+x y(x)+y(x)^2\right ) y'(x)^2+y'(x)^3=0 \] ODE Classification
[_quadrature]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.201549 (sec), leaf count = 43
\[\left \{\left \{y(x)\to -\frac {1}{x+c_1}\right \},\left \{y(x)\to c_1 e^{\frac {x^2}{2}}\right \},\left \{y(x)\to \frac {x^3}{3}+c_1\right \}\right \}\]
Maple ✓
cpu = 0.046 (sec), leaf count = 32
\[\left [y \left (x \right ) = \frac {x^{3}}{3}+\textit {\_C1}, y \left (x \right ) = \frac {1}{-x +\textit {\_C1}}, y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{\frac {x^{2}}{2}}\right ]\] Mathematica raw input
DSolve[-(x^3*y[x]^3) + x*y[x]*(x^2 + x*y[x] + y[x]^2)*y'[x] - (x^2 + x*y[x] + y[x]^2)*y'[x]^2 + y'[x]^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(x + C[1])^(-1)}, {y[x] -> E^(x^2/2)*C[1]}, {y[x] -> x^3/3 + C[1]}}
Maple raw input
dsolve(diff(y(x),x)^3-(x^2+x*y(x)+y(x)^2)*diff(y(x),x)^2+x*y(x)*(x^2+x*y(x)+y(x)^2)*diff(y(x),x)-x^3*y(x)^3 = 0, y(x))
Maple raw output
[y(x) = 1/3*x^3+_C1, y(x) = 1/(-x+_C1), y(x) = _C1*exp(1/2*x^2)]