4.36.45 $y^{″}(x)=y^{\prime }(x)(\text{f0}(x)y(x)+\text{f1}(x))+\text{g0}(x)y(x{)}^3+\text{g1}(x)y(x{)}^2+\text{g2}(x)y(x)+\text{g3}(x)$

ODE
$$y^{″}(x)=y^{\prime }(x)(\text{f0}(x)y(x)+\text{f1}(x))+\text{g0}(x)y(x{)}^3+\text{g1}(x)y(x{)}^2+\text{g2}(x)y(x)+\text{g3}(x)$$ ODE Classification

[NONE]

Book solution method
TO DO

Mathematica ✗
cpu = 0.60001 (sec), leaf count = 0 , could not solve

DSolve[Derivative[2][y][x] == g3[x] + g2[x]*y[x] + g1[x]*y[x]^2 + g0[x]*y[x]^3 + (f1[x] + f0[x]*y[x])*Derivative[1][y][x], y[x], x]

Maple ✗
cpu = 1.124 (sec), leaf count = 0 , could not solve

dsolve(diff(diff(y(x),x),x) = (f0(x)*y(x)+f1(x))*diff(y(x),x)+g0(x)*y(x)^3+g1(x)*y(x)^2+g2(x)*y(x)+g3(x), y(x),'implicit')

Mathematica raw input

DSolve[y''[x] == g3[x] + g2[x]*y[x] + g1[x]*y[x]^2 + g0[x]*y[x]^3 + (f1[x] + f0[x]*y[x])*y'[x],y[x],x]

Mathematica raw output

DSolve[Derivative[2][y][x] == g3[x] + g2[x]*y[x] + g1[x]*y[x]^2 + g0[x]*y[x]^3 +
 (f1[x] + f0[x]*y[x])*Derivative[1][y][x], y[x], x]

Maple raw input

dsolve(diff(diff(y(x),x),x) = (f0(x)*y(x)+f1(x))*diff(y(x),x)+g0(x)*y(x)^3+g1(x)*y(x)^2+g2(x)*y(x)+g3(x), y(x),'implicit')

Maple raw output

dsolve(diff(diff(y(x),x),x) = (f0(x)*y(x)+f1(x))*diff(y(x),x)+g0(x)*y(x)^3+g1(x)
*y(x)^2+g2(x)*y(x)+g3(x), y(x),'implicit')