ODE
\[ a y(x) \left (1-y(x)^n\right )+x^2 y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 28.6427 (sec), leaf count = 0 , could not solve
DSolve[a*y[x]*(1 - y[x]^n) + x^2*Derivative[2][y][x] == 0, y[x], x]
Maple ✗
cpu = 4.89 (sec), leaf count = 0 , result contains DESol or ODESolStruc
\[[]\]
Mathematica raw input
DSolve[a*y[x]*(1 - y[x]^n) + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[a*y[x]*(1 - y[x]^n) + x^2*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+a*y(x)*(1-y(x)^n) = 0, y(x))
Maple raw output
[]