ODE
\[ 9 \left (1-x^2\right ) y(x)^4 y'(x)^2+4 x^2+6 x y(x)^5 y'(x)=0 \] ODE Classification
[[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
Book solution method
Change of variable
Mathematica ✓
cpu = 0.479874 (sec), leaf count = 34
\[\left \{y(x)\to -\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{-4 x^2+4+c_1{}^2}}{\sqrt [3]{c_1}}\right \}\]
Maple ✓
cpu = 3.16 (sec), leaf count = 245
\[\left [y \left (x \right ) = \left (-4 x^{2}+4\right )^{\frac {1}{6}}, y \left (x \right ) = -\left (-4 x^{2}+4\right )^{\frac {1}{6}}, y \left (x \right ) = \left (-\frac {1}{2}-\frac {i \sqrt {3}}{2}\right ) \left (-4 x^{2}+4\right )^{\frac {1}{6}}, y \left (x \right ) = \left (-\frac {1}{2}+\frac {i \sqrt {3}}{2}\right ) \left (-4 x^{2}+4\right )^{\frac {1}{6}}, y \left (x \right ) = \left (\frac {1}{2}-\frac {i \sqrt {3}}{2}\right ) \left (-4 x^{2}+4\right )^{\frac {1}{6}}, y \left (x \right ) = \left (\frac {1}{2}+\frac {i \sqrt {3}}{2}\right ) \left (-4 x^{2}+4\right )^{\frac {1}{6}}, y \left (x \right ) = \frac {\left (\left (-16 \textit {\_C1}^{2}+4 x^{2}-4\right ) \textit {\_C1}^{2}\right )^{\frac {1}{3}}}{2 \textit {\_C1}}, y \left (x \right ) = -\frac {\left (\left (-16 \textit {\_C1}^{2}+4 x^{2}-4\right ) \textit {\_C1}^{2}\right )^{\frac {1}{3}}}{4 \textit {\_C1}}-\frac {i \sqrt {3}\, \left (\left (-16 \textit {\_C1}^{2}+4 x^{2}-4\right ) \textit {\_C1}^{2}\right )^{\frac {1}{3}}}{4 \textit {\_C1}}, y \left (x \right ) = -\frac {\left (\left (-16 \textit {\_C1}^{2}+4 x^{2}-4\right ) \textit {\_C1}^{2}\right )^{\frac {1}{3}}}{4 \textit {\_C1}}+\frac {i \sqrt {3}\, \left (\left (-16 \textit {\_C1}^{2}+4 x^{2}-4\right ) \textit {\_C1}^{2}\right )^{\frac {1}{3}}}{4 \textit {\_C1}}\right ]\] Mathematica raw input
DSolve[4*x^2 + 6*x*y[x]^5*y'[x] + 9*(1 - x^2)*y[x]^4*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{y[x] -> -(((-1/2)^(1/3)*(4 - 4*x^2 + C[1]^2)^(1/3))/C[1]^(1/3))}
Maple raw input
dsolve(9*(-x^2+1)*y(x)^4*diff(y(x),x)^2+6*x*y(x)^5*diff(y(x),x)+4*x^2 = 0, y(x))
Maple raw output
[y(x) = (-4*x^2+4)^(1/6), y(x) = -(-4*x^2+4)^(1/6), y(x) = (-1/2-1/2*I*3^(1/2))*(-4*x^2+4)^(1/6), y(x) = (-1/2+1/2*I*3^(1/2))*(-4*x^2+4)^(1/6), y(x) = (1/2-1/2*I*3^(1/2))*(-4*x^2+4)^(1/6), y(x) = (1/2+1/2*I*3^(1/2))*(-4*x^2+4)^(1/6), y(x) = 1/2/_C1*((-16*_C1^2+4*x^2-4)*_C1^2)^(1/3), y(x) = -1/4/_C1*((-16*_C1^2+4*x^2-4)*_C1^2)^(1/3)-1/4*I*3^(1/2)/_C1*((-16*_C1^2+4*x^2-4)*_C1^2)^(1/3), y(x) = -1/4/_C1*((-16*_C1^2+4*x^2-4)*_C1^2)^(1/3)+1/4*I*3^(1/2)/_C1*((-16*_C1^2+4*x^2-4)*_C1^2)^(1/3)]