ODE No. 1754

\[ n y(x) y''(x)+(1-n) y'(x)^2=0 \]

✓ Mathematica : cpu = 0.131309 (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 = 0.054 (sec), leaf count = 15

dsolve(n*y(x)*diff(diff(y(x),x),x)-(n-1)*diff(y(x),x)^2=0,y(x))

\[y \left (x \right ) = \left (\frac {x c_{1} +c_{2}}{n}\right )^{n}\]