2.554   ODE No. 554

\[ x^{n-1} y'(x)^n-n x y'(x)+y(x)=0 \] Mathematica : cpu = 0.150736 (sec), leaf count = 54


\[\text {Solve}\left [\left \{y(x)=\frac {n x^2 K[1]-x^n K[1]^n}{x},x=c_1 (K[1]-n K[1])^{\frac {n}{1-n}}\right \},\{y(x),K[1]\}\right ]\] Maple : cpu = 0.449 (sec), leaf count = 32


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