4.43.8 y(x)+y(x)f(x)+2f(x)y(x)=0

ODE
y(x)+y(x)f(x)+2f(x)y(x)=0 ODE Classification

(ODEtools/info) missing specification of intermediate function

Book solution method
TO DO

Mathematica
cpu = 0.125296 (sec), leaf count = 0 , could not solve

DSolve[y[x]*Derivative[1][f][x] + 2*f[x]*Derivative[1][y][x] + Derivative[3][y][x] == 0, y[x], x]

Maple
cpu = 0.114 (sec), leaf count = 0 , result contains DESol

{y(x)=(DESol({d2dx2_Y(x)+f(x)_Y(x)2},{_Y(x)}))2}

Mathematica raw input

DSolve[y[x]*f'[x] + 2*f[x]*y'[x] + y'''[x] == 0,y[x],x]

Mathematica raw output

DSolve[y[x]*Derivative[1][f][x] + 2*f[x]*Derivative[1][y][x] + Derivative[3][y][
x] == 0, y[x], x]

Maple raw input

dsolve(diff(diff(diff(y(x),x),x),x)+2*f(x)*diff(y(x),x)+diff(f(x),x)*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = DESol({diff(diff(_Y(x),x),x)+1/2*f(x)*_Y(x)},{_Y(x)})^2