\[ n y(x) y''(x)+(1-n) y'(x)^2=0 \] ✓ Mathematica : cpu = 0.122622 (sec), leaf count = 17
DSolve[(1 - n)*Derivative[1][y][x]^2 + n*y[x]*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_2 (x-c_1 n){}^n\right \}\right \}\] ✓ Maple : cpu = 0.915 (sec), leaf count = 15
dsolve(n*y(x)*diff(diff(y(x),x),x)-(n-1)*diff(y(x),x)^2=0,y(x))
\[y \left (x \right ) = \left (\frac {c_{1} x +c_{2}}{n}\right )^{n}\]