4.36.44 $y^{″}(x)=(3\text{f1}(x)-y(x))y^{\prime }(x)+\text{f1}(x)y(x{)}^2+\text{f2}(x)+\text{f3}(x)y(x)+y(x{)}^3$

ODE
$$y^{″}(x)=(3\text{f1}(x)-y(x))y^{\prime }(x)+\text{f1}(x)y(x{)}^2+\text{f2}(x)+\text{f3}(x)y(x)+y(x{)}^3$$ ODE Classification

[NONE]

Book solution method
TO DO

Mathematica ✗
cpu = 0.403089 (sec), leaf count = 0 , could not solve

DSolve[Derivative[2][y][x] == f2[x] + f3[x]*y[x] + f1[x]*y[x]^2 + y[x]^3 + (3*f1[x] - y[x])*Derivative[1][y][x], y[x], x]

Maple ✗
cpu = 0.371 (sec), leaf count = 0 , could not solve

dsolve(diff(diff(y(x),x),x) = (3*f1(x)-y(x))*diff(y(x),x)+f2(x)+f3(x)*y(x)+f1(x)*y(x)^2+y(x)^3, y(x),'implicit')

Mathematica raw input

DSolve[y''[x] == f2[x] + f3[x]*y[x] + f1[x]*y[x]^2 + y[x]^3 + (3*f1[x] - y[x])*y'[x],y[x],x]

Mathematica raw output

DSolve[Derivative[2][y][x] == f2[x] + f3[x]*y[x] + f1[x]*y[x]^2 + y[x]^3 + (3*f1
[x] - y[x])*Derivative[1][y][x], y[x], x]

Maple raw input

dsolve(diff(diff(y(x),x),x) = (3*f1(x)-y(x))*diff(y(x),x)+f2(x)+f3(x)*y(x)+f1(x)*y(x)^2+y(x)^3, y(x),'implicit')

Maple raw output

dsolve(diff(diff(y(x),x),x) = (3*f1(x)-y(x))*diff(y(x),x)+f2(x)+f3(x)*y(x)+f1(x)
*y(x)^2+y(x)^3, y(x),'implicit')