\[ \boxed { ny \left ( x \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) - \left ( n-1 \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 0.033504 (sec), leaf count = 17 \[ \left \{\left \{y(x)\to c_2 \left (x-c_1 n\right ){}^n\right \}\right \} \]
Maple: cpu = 1.544 (sec), leaf count = 15 \[ \left \{ y \left ( x \right ) = \left ( {\frac {{\it \_C1}\,x+{\it \_C2} }{n}} \right ) ^{n} \right \} \]