4.2.39 \(y'(x)=y(x)^2-a x \left (1-x^{n-1}\right ) y(x)^3\)

ODE
\[ y'(x)=y(x)^2-a x \left (1-x^{n-1}\right ) y(x)^3 \] ODE Classification

[_Abel]

Book solution method
Abel ODE, First kind

Mathematica
cpu = 32.8836 (sec), leaf count = 0 , could not solve

DSolve[Derivative[1][y][x] == y[x]^2 - a*x*(1 - x^(-1 + n))*y[x]^3, y[x], x]

Maple
cpu = 2.908 (sec), leaf count = 0 , could not solve

dsolve(diff(y(x),x) = y(x)^2-a*x*(1-x^(n-1))*y(x)^3, y(x),'implicit')

Mathematica raw input

DSolve[y'[x] == y[x]^2 - a*x*(1 - x^(-1 + n))*y[x]^3,y[x],x]

Mathematica raw output

DSolve[Derivative[1][y][x] == y[x]^2 - a*x*(1 - x^(-1 + n))*y[x]^3, y[x], x]

Maple raw input

dsolve(diff(y(x),x) = y(x)^2-a*x*(1-x^(n-1))*y(x)^3, y(x),'implicit')

Maple raw output

dsolve(diff(y(x),x) = y(x)^2-a*x*(1-x^(n-1))*y(x)^3, y(x),'implicit')