\[ -x^{-a} y(x)+a x^{-a-1}-x^{-2 a}-x^a y(x)^3+y'(x)+3 y(x)^2=0 \] ✓ Mathematica : cpu = 0.313116 (sec), leaf count = 228
\[\left \{\left \{y(x)\to x^{-a}-\frac {e^{-\frac {2 x^{1-a}}{1-a}}}{\sqrt {-\frac {2^{\frac {2 (a+1)}{a-1}+1} x^{a+1} \left (\frac {x^{1-a}}{1-a}\right )^{\frac {a+1}{a-1}} \Gamma \left (\frac {a+1}{1-a},-\frac {4 x^{1-a}}{a-1}\right )}{a-1}+c_1}}\right \},\left \{y(x)\to x^{-a}+\frac {e^{-\frac {2 x^{1-a}}{1-a}}}{\sqrt {-\frac {2^{\frac {2 (a+1)}{a-1}+1} x^{a+1} \left (\frac {x^{1-a}}{1-a}\right )^{\frac {a+1}{a-1}} \Gamma \left (\frac {a+1}{1-a},-\frac {4 x^{1-a}}{a-1}\right )}{a-1}+c_1}}\right \}\right \}\] ✓ Maple : cpu = 0.119 (sec), leaf count = 956
\[\left \{y \left (x \right ) = x^{-a}-\frac {{\mathrm e}^{\frac {2 x \,x^{-a}}{a -1}}}{\sqrt {-\frac {2 \left (-\frac {\left (a -1\right ) \left (-\frac {4 a^{2} x^{-a +1}}{-a +1}+\frac {8 a \,x^{-a +1}}{-a +1}+2 a -\frac {4 x^{-a +1}}{-a +1}-2\right ) \left (-a +1\right ) 2^{\frac {2 a}{-a +1}-3+\frac {2}{-a +1}+\frac {2}{a -1}} x^{-\frac {a^{2}}{-a +1}+a +\frac {1}{-a +1}-1} \left (\frac {1}{-a +1}\right )^{-\frac {a +1}{a -1}} \left (\frac {x^{-a +1}}{-a +1}\right )^{\frac {1}{a -1}} \WhittakerM \left (-\frac {a}{a -1}, -\frac {1}{a -1}+\frac {1}{2}, -\frac {4 x^{-a +1}}{a -1}\right ) {\mathrm e}^{\frac {2 x^{-a +1}}{a -1}}}{\left (a +1\right ) \left (a -3\right )}+\frac {\left (a -1\right ) \left (-a +1\right ) 2^{\frac {2 a}{-a +1}-1+\frac {2}{-a +1}+\frac {2}{a -1}} x^{-\frac {a^{2}}{-a +1}+a +\frac {1}{-a +1}-1} \left (\frac {1}{-a +1}\right )^{-\frac {a +1}{a -1}} \left (\frac {x^{-a +1}}{-a +1}\right )^{\frac {1}{a -1}} \WhittakerM \left (-\frac {1}{a -1}, -\frac {1}{a -1}+\frac {1}{2}, -\frac {4 x^{-a +1}}{a -1}\right ) {\mathrm e}^{\frac {2 x^{-a +1}}{a -1}}}{\left (a +1\right ) \left (a -3\right )}\right ) 2^{-\frac {2 a}{-a +1}-\frac {2}{-a +1}} \left (\frac {1}{-a +1}\right )^{\frac {a +1}{a -1}}}{-a +1}+c_{1}}}, y \left (x \right ) = x^{-a}+\frac {{\mathrm e}^{\frac {2 x \,x^{-a}}{a -1}}}{\sqrt {-\frac {2 \left (-\frac {\left (a -1\right ) \left (-\frac {4 a^{2} x^{-a +1}}{-a +1}+\frac {8 a \,x^{-a +1}}{-a +1}+2 a -\frac {4 x^{-a +1}}{-a +1}-2\right ) \left (-a +1\right ) 2^{\frac {2 a}{-a +1}-3+\frac {2}{-a +1}+\frac {2}{a -1}} x^{-\frac {a^{2}}{-a +1}+a +\frac {1}{-a +1}-1} \left (\frac {1}{-a +1}\right )^{-\frac {a +1}{a -1}} \left (\frac {x^{-a +1}}{-a +1}\right )^{\frac {1}{a -1}} \WhittakerM \left (-\frac {a}{a -1}, -\frac {1}{a -1}+\frac {1}{2}, -\frac {4 x^{-a +1}}{a -1}\right ) {\mathrm e}^{\frac {2 x^{-a +1}}{a -1}}}{\left (a +1\right ) \left (a -3\right )}+\frac {\left (a -1\right ) \left (-a +1\right ) 2^{\frac {2 a}{-a +1}-1+\frac {2}{-a +1}+\frac {2}{a -1}} x^{-\frac {a^{2}}{-a +1}+a +\frac {1}{-a +1}-1} \left (\frac {1}{-a +1}\right )^{-\frac {a +1}{a -1}} \left (\frac {x^{-a +1}}{-a +1}\right )^{\frac {1}{a -1}} \WhittakerM \left (-\frac {1}{a -1}, -\frac {1}{a -1}+\frac {1}{2}, -\frac {4 x^{-a +1}}{a -1}\right ) {\mathrm e}^{\frac {2 x^{-a +1}}{a -1}}}{\left (a +1\right ) \left (a -3\right )}\right ) 2^{-\frac {2 a}{-a +1}-\frac {2}{-a +1}} \left (\frac {1}{-a +1}\right )^{\frac {a +1}{a -1}}}{-a +1}+c_{1}}}\right \}\]