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 = 62.9996 (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 = 2.083 (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))
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))
Maple raw output
dsolve(diff(y(x),x) = a*y(x)^2+x*y(x)^3*(b+c*x^(n-1)), y(x))