ODE No. 328

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

✓ Mathematica : cpu = 0.240412 (sec), leaf count = 42

DSolve[y[x] - 2*x*Derivative[1][y][x] + a*x^2*y[x]^n*Derivative[1][y][x] == 0,y[x],x]

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

✓ Maple : cpu = 0.305 (sec), leaf count = 33

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

\[\left (y \left (x \right )^{n} a x -n -2\right )^{n} y \left (x \right )^{2 n} x^{-n}-c_{1} = 0\]