\[ \boxed { {x}^{n}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -a \left ( y \left ( x \right ) \right ) ^{2}-b{x}^{2\,n-2}=0} \]
Mathematica: cpu = 0.070009 (sec), leaf count = 328 \[ \left \{\left \{y(x)\to -\frac {x^n \left (\frac {1}{2} \sqrt {a} \sqrt {b} c_1 \left (-\frac {n-1}{\sqrt {a} \sqrt {b}}-\sqrt {\frac {(n-1)^2}{a b}-4}\right ) x^{\frac {1}{2} \sqrt {a} \sqrt {b} \left (-\frac {n-1}{\sqrt {a} \sqrt {b}}-\sqrt {\frac {(n-1)^2}{a b}-4}\right )-1}+\frac {1}{2} \sqrt {a} \sqrt {b} \left (\sqrt {\frac {(n-1)^2}{a b}-4}-\frac {n-1}{\sqrt {a} \sqrt {b}}\right ) x^{\frac {1}{2} \sqrt {a} \sqrt {b} \left (\sqrt {\frac {(n-1)^2}{a b}-4}-\frac {n-1}{\sqrt {a} \sqrt {b}}\right )-1}\right )}{a \left (c_1 x^{\frac {1}{2} \sqrt {a} \sqrt {b} \left (-\frac {n-1}{\sqrt {a} \sqrt {b}}-\sqrt {\frac {(n-1)^2}{a b}-4}\right )}+x^{\frac {1}{2} \sqrt {a} \sqrt {b} \left (\sqrt {\frac {(n-1)^2}{a b}-4}-\frac {n-1}{\sqrt {a} \sqrt {b}}\right )}\right )}\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 88 \[ \left \{ y \left ( x \right ) ={\frac {1}{2\,a} \left ( -{x}^{n-1}\tan \left ( -{\frac {\ln \left ( x \right ) }{2}\sqrt {4\,ab-{n}^{2}+2\,n-1 }}+{\frac {{\it \_C1}}{2}\sqrt {4\,ab-{n}^{2}+2\,n-1}} \right ) \sqrt { 4\,ab-{n}^{2}+2\,n-1}+{x}^{n-1}n-{x}^{n-1} \right ) } \right \} \]