4.38.13 \(a y(x) \left (1-y(x)^n\right )+x^2 y''(x)=0\)

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

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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

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