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 = 59.3771 (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 = 2.216 (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))
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))
Maple raw output
dsolve(diff(y(x),x) = y(x)^2-a*x*(1-x^(n-1))*y(x)^3, y(x))