4.1786   y′′(x) = f(y(x))

ODE

y′′(x) = f(y(x))

ODE Classification

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Book solution method
TO DO

Mathematica
cpu = 0.905141 (sec), leaf count = 38

    ⌊           (                                  )      ⌋
                 ∫ y(x)
Solve⌈ (c2 + x)2 = (     ∘--∫-------1-----------dK [2]) 2,y(x)⌉
                   1     2 K1 [2]f(K[1])dK [1]+ c1

Maple
cpu = 0.083 (sec), leaf count = 51

(                                                                                )
{ ∫ y(x)         1                        ∫ y(x)           1                       }
(      ∘---∫-------------d-b− x− -C2 = 0,     −  ∘--∫-------------d-b− x − C2 = 0)
         2  f ( b)d-b+ C1                         2  f ( b)d-b+-C1

Mathematica raw input

DSolve[y''[x] == f[y[x]],y[x],x]

Mathematica raw output

Solve[(x + C[2])^2 == Integrate[1/Sqrt[C[1] + 2*Integrate[f[K[1]], {K[1], 1, K[2
]}]], {K[2], 1, y[x]}]^2, y[x]]

Maple raw input

dsolve(diff(diff(y(x),x),x) = f(y(x)), y(x),'implicit')

Maple raw output

Intat(1/(2*Int(f(_b),_b)+_C1)^(1/2),_b = y(x))-x-_C2 = 0, Intat(-1/(2*Int(f(_b),
_b)+_C1)^(1/2),_b = y(x))-x-_C2 = 0