4.2.40 \(y'(x)=a y(x)^2+x y(x)^3 \left (b+c x^{n-1}\right )\)

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

[_Abel]

Book solution method
Abel ODE, First kind

Mathematica
cpu = 36.5386 (sec), leaf count = 0 , could not solve

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

Maple
cpu = 2.416 (sec), leaf count = 0 , could not solve

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

Mathematica raw input

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

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