4.2.37 \(y'(x)=y(x)^2 \left (x^3 y(x)+1\right )\)

ODE
\[ y'(x)=y(x)^2 \left (x^3 y(x)+1\right ) \] ODE Classification

[_Abel]

Book solution method
Abel ODE, First kind

Mathematica
cpu = 22.8741 (sec), leaf count = 0 , could not solve

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

Maple
cpu = 3.194 (sec), leaf count = 0 , could not solve

dsolve(diff(y(x),x) = (1+x^3*y(x))*y(x)^2, y(x),'implicit')

Mathematica raw input

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

Mathematica raw output

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

Maple raw input

dsolve(diff(y(x),x) = (1+x^3*y(x))*y(x)^2, y(x),'implicit')

Maple raw output

dsolve(diff(y(x),x) = (1+x^3*y(x))*y(x)^2, y(x),'implicit')