ODE
\[ \left (a-x^3-y(x)^3\right ) y'(x)+x^2 y(x)+x y(x)^2 y'(x)^2=0 \] ODE Classification
[_rational]
Book solution method
Change of variable
Mathematica ✓
cpu = 0.222173 (sec), leaf count = 31
\[\left \{y(x)\to \frac {\sqrt [3]{a+(-1+c_1) x^3}}{\sqrt [3]{1-\frac {1}{c_1}}}\right \}\]
Maple ✓
cpu = 1.441 (sec), leaf count = 303
\[\left [y \left (x \right ) = \left (x^{3}+a -2 x \sqrt {a x}\right )^{\frac {1}{3}}, y \left (x \right ) = \left (x^{3}+a +2 x \sqrt {a x}\right )^{\frac {1}{3}}, y \left (x \right ) = -\frac {\left (x^{3}+a -2 x \sqrt {a x}\right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (x^{3}+a -2 x \sqrt {a x}\right )^{\frac {1}{3}}}{2}, y \left (x \right ) = -\frac {\left (x^{3}+a -2 x \sqrt {a x}\right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (x^{3}+a -2 x \sqrt {a x}\right )^{\frac {1}{3}}}{2}, y \left (x \right ) = -\frac {\left (x^{3}+a +2 x \sqrt {a x}\right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (x^{3}+a +2 x \sqrt {a x}\right )^{\frac {1}{3}}}{2}, y \left (x \right ) = -\frac {\left (x^{3}+a +2 x \sqrt {a x}\right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (x^{3}+a +2 x \sqrt {a x}\right )^{\frac {1}{3}}}{2}, \int _{\textit {\_b}}^{y \left (x \right )}\frac {\textit {\_a}^{2}}{\sqrt {\textit {\_a}^{6}+\left (-2 x^{3}-2 a \right ) \textit {\_a}^{3}+\left (-x^{3}+a \right )^{2}}}d \textit {\_a} +\frac {\ln \left (x \right )}{2}-\textit {\_C1} = 0, \int _{\textit {\_b}}^{y \left (x \right )}\frac {\textit {\_a}^{2}}{\sqrt {\textit {\_a}^{6}+\left (-2 x^{3}-2 a \right ) \textit {\_a}^{3}+\left (-x^{3}+a \right )^{2}}}d \textit {\_a} -\frac {\ln \left (x \right )}{2}-\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[x^2*y[x] + (a - x^3 - y[x]^3)*y'[x] + x*y[x]^2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{y[x] -> (a + x^3*(-1 + C[1]))^(1/3)/(1 - C[1]^(-1))^(1/3)}
Maple raw input
dsolve(x*y(x)^2*diff(y(x),x)^2+(a-x^3-y(x)^3)*diff(y(x),x)+x^2*y(x) = 0, y(x))
Maple raw output
[y(x) = (x^3+a-2*x*(a*x)^(1/2))^(1/3), y(x) = (x^3+a+2*x*(a*x)^(1/2))^(1/3), y(x) = -1/2*(x^3+a-2*x*(a*x)^(1/2))^(1/3)-1/2*I*3^(1/2)*(x^3+a-2*x*(a*x)^(1/2))^(1/3), y(x) = -1/2*(x^3+a-2*x*(a*x)^(1/2))^(1/3)+1/2*I*3^(1/2)*(x^3+a-2*x*(a*x)^(1/2))^(1/3), y(x) = -1/2*(x^3+a+2*x*(a*x)^(1/2))^(1/3)-1/2*I*3^(1/2)*(x^3+a+2*x*(a*x)^(1/2))^(1/3), y(x) = -1/2*(x^3+a+2*x*(a*x)^(1/2))^(1/3)+1/2*I*3^(1/2)*(x^3+a+2*x*(a*x)^(1/2))^(1/3), Int(_a^2/(_a^6+(-2*x^3-2*a)*_a^3+(-x^3+a)^2)^(1/2),_a = _b .. y(x))+1/2*ln(x)-_C1 = 0, Int(_a^2/(_a^6+(-2*x^3-2*a)*_a^3+(-x^3+a)^2)^(1/2),_a = _b .. y(x))-1/2*ln(x)-_C1 = 0]