\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +{x}^{-a-1} \left ( y \left ( x \right ) \right ) ^{2}-{x}^{a}=0} \]
Mathematica: cpu = 0.065008 (sec), leaf count = 230 \[ \left \{\left \{y(x)\to \frac {x^{a+1} \left (c_1 \left (\frac {1}{2} x^{-\frac {a}{2}-\frac {1}{2}} \Gamma (a+1) \left (I_{a-1}\left (2 \sqrt {x}\right )+I_{a+1}\left (2 \sqrt {x}\right )\right )-\frac {1}{2} a x^{-\frac {a}{2}-1} \Gamma (a+1) I_a\left (2 \sqrt {x}\right )\right )-\frac {1}{2} (-1)^{-a} a x^{-\frac {a}{2}-1} \Gamma (1-a) I_{-a}\left (2 \sqrt {x}\right )+\frac {1}{2} (-1)^{-a} x^{-\frac {a}{2}-\frac {1}{2}} \Gamma (1-a) \left (I_{-a-1}\left (2 \sqrt {x}\right )+I_{1-a}\left (2 \sqrt {x}\right )\right )\right )}{c_1 x^{-a/2} \Gamma (a+1) I_a\left (2 \sqrt {x}\right )+(-1)^{-a} x^{-a/2} \Gamma (1-a) I_{-a}\left (2 \sqrt {x}\right )}\right \}\right \} \]
Maple: cpu = 0.078 (sec), leaf count = 81 \[ \left \{ y \left ( x \right ) =-{{\it \_C1}\,{x}^{a+1}{{\sl K}_{a+1 }\left (2\,\sqrt {x}\right )}{\frac {1}{\sqrt {x}}} \left ( {{\sl K}_{a }\left (2\,\sqrt {x}\right )}{\it \_C1}+{{\sl I}_{a}\left (2\,\sqrt {x} \right )} \right ) ^{-1}}+{{x}^{a+1}{{\sl I}_{a+1}\left (2\,\sqrt {x} \right )}{\frac {1}{\sqrt {x}}} \left ( {{\sl K}_{a}\left (2\,\sqrt {x} \right )}{\it \_C1}+{{\sl I}_{a}\left (2\,\sqrt {x}\right )} \right ) ^{-1 }} \right \} \]
Sage: cpu = 0.236 (sec), leaf count = 0 \[ \left [\left [y\left (x\right ) = -\frac {{\left ({\left (c \operatorname {Y_{a}}(2 \, \sqrt {-x}) + \operatorname {J_{a}}(2 \, \sqrt {-x})\right )} a + {\left (c \operatorname {Y_{a + 1}}(2 \, \sqrt {-x}) - c \operatorname {Y_{a - 1}}(2 \, \sqrt {-x}) + \operatorname {J_{a + 1}}(2 \, \sqrt {-x}) - \operatorname {J_{a - 1}}(2 \, \sqrt {-x})\right )} \sqrt {-x}\right )} x^{a}}{2 \, {\left (c \operatorname {Y_{a}}(2 \, \sqrt {-x}) + \operatorname {J_{a}}(2 \, \sqrt {-x})\right )}}\right ], \text {\texttt {riccati}}\right ] \]