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 = 0.00723968 (sec), leaf count = 43
\[\left \{\left \{y(x)\to -\frac {1}{c_1+x}\right \},\left \{y(x)\to c_1 e^{\frac {x^2}{2}}\right \},\left \{y(x)\to c_1+\frac {x^3}{3}\right \}\right \}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 33
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{-1}+x-{\it \_C1}=0,y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{{\frac {{x}^{2}}{2}}}},y \left ( x \right ) ={\frac {{x}^{3}}{3}}+{\it \_C1} \right \} \] 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),'implicit')
Maple raw output
y(x) = 1/3*x^3+_C1, 1/y(x)+x-_C1 = 0, y(x) = _C1*exp(1/2*x^2)