\[ \boxed { {x}^{n}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{2}- \left ( n-1 \right ) {x}^{n-1}y \left ( x \right ) +{x}^{2\,n-2}=0} \]
Mathematica: cpu = 0.029004 (sec), leaf count = 19 \[ \left \{\left \{y(x)\to x^{n-1} \tan \left (c_1-\log (x)\right )\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 17 \[ \left \{ y \left ( x \right ) =\tan \left ( -\ln \left ( x \right ) +{\it \_C1} \right ) {x}^{n-1} \right \} \]