2.554   ODE No. 554

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

✓ Mathematica : cpu = 0.128068 (sec), leaf count = 54

DSolve[y[x] - n*x*Derivative[1][y][x] + x^(-1 + n)*Derivative[1][y][x]^n == 0,y[x],x]
 

\[\text {Solve}\left [\left \{y(x)=\frac {n x^2 K[1]-x^n K[1]^n}{x},x=c_1 (K[1]-n K[1])^{\frac {n}{1-n}}\right \},\{y(x),K[1]\}\right ]\]

✓ Maple : cpu = 0.292 (sec), leaf count = 40

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

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