ODE
\[ -x^3 y(x)^6+x \left (x^2+y(x)^4+x y(x)^2\right ) y(x)^2 y'(x)-\left (x^2+y(x)^4+x y(x)^2\right ) y'(x)^2+y'(x)^3=0 \] ODE Classification
[_quadrature]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.269678 (sec), leaf count = 105
\[\left \{\left \{y(x)\to -\frac {\sqrt [3]{-\frac {1}{3}}}{\sqrt [3]{-x-c_1}}\right \},\left \{y(x)\to \frac {1}{\sqrt [3]{3} \sqrt [3]{-x-c_1}}\right \},\left \{y(x)\to \frac {(-1)^{2/3}}{\sqrt [3]{3} \sqrt [3]{-x-c_1}}\right \},\left \{y(x)\to \frac {x^3}{3}+c_1\right \},\left \{y(x)\to -\frac {2}{x^2+2 c_1}\right \}\right \}\]
Maple ✓
cpu = 0.11 (sec), leaf count = 89
\[\left [y \left (x \right ) = \frac {x^{3}}{3}+\textit {\_C1}, y \left (x \right ) = \frac {1}{\left (-3 x +\textit {\_C1} \right )^{\frac {1}{3}}}, y \left (x \right ) = -\frac {1}{2 \left (-3 x +\textit {\_C1} \right )^{\frac {1}{3}}}-\frac {i \sqrt {3}}{2 \left (-3 x +\textit {\_C1} \right )^{\frac {1}{3}}}, y \left (x \right ) = -\frac {1}{2 \left (-3 x +\textit {\_C1} \right )^{\frac {1}{3}}}+\frac {i \sqrt {3}}{2 \left (-3 x +\textit {\_C1} \right )^{\frac {1}{3}}}, y \left (x \right ) = \frac {2}{-x^{2}+2 \textit {\_C1}}\right ]\] Mathematica raw input
DSolve[-(x^3*y[x]^6) + x*y[x]^2*(x^2 + x*y[x]^2 + y[x]^4)*y'[x] - (x^2 + x*y[x]^2 + y[x]^4)*y'[x]^2 + y'[x]^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -((-1/3)^(1/3)/(-x - C[1])^(1/3))}, {y[x] -> 1/(3^(1/3)*(-x - C[1])^(1/3))}, {y[x] -> (-1)^(2/3)/(3^(1/3)*(-x - C[1])^(1/3))}, {y[x] -> x^3/3 + C[1]}, {y[x] -> -2/(x^2 + 2*C[1])}}
Maple raw input
dsolve(diff(y(x),x)^3-(x^2+x*y(x)^2+y(x)^4)*diff(y(x),x)^2+x*y(x)^2*(x^2+x*y(x)^2+y(x)^4)*diff(y(x),x)-x^3*y(x)^6 = 0, y(x))
Maple raw output
[y(x) = 1/3*x^3+_C1, y(x) = 1/(-3*x+_C1)^(1/3), y(x) = -1/2/(-3*x+_C1)^(1/3)-1/2*I*3^(1/2)/(-3*x+_C1)^(1/3), y(x) = -1/2/(-3*x+_C1)^(1/3)+1/2*I*3^(1/2)/(-3*x+_C1)^(1/3), y(x) = 2/(-x^2+2*_C1)]