4.1815   ay(x)y′(x)2 + by(x)+ y′′(x) = 0

ODE

ay(x)y′(x)2 + by(x)+ y′′(x) = 0

ODE Classification

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

Book solution method
TO DO

Mathematica
cpu = 200.27 (sec), leaf count = 0 , could not solve

DSolve[b*y[x] + a*y[x]*Derivative[1][y][x]^2 + Derivative[2][y][x] == 0, y[x], x]

Maple
cpu = 0.167 (sec), leaf count = 70

(                                                                                  )
{ ∫ y(x)         1                         ∫ y(x)            1                       }
       a∘--(-------------)d-a− x− -C2 = 0,     − a ∘--(------------)d-a− x − C2 = 0
(         a e−-a2a C1a − b                          a  e− a2a-C1a− b               )

Mathematica raw input

DSolve[b*y[x] + a*y[x]*y'[x]^2 + y''[x] == 0,y[x],x]

Mathematica raw output

DSolve[b*y[x] + a*y[x]*Derivative[1][y][x]^2 + Derivative[2][y][x] == 0, y[x], x
]

Maple raw input

dsolve(diff(diff(y(x),x),x)+a*y(x)*diff(y(x),x)^2+b*y(x) = 0, y(x),'implicit')

Maple raw output

Intat(a/(a*(exp(-_a^2*a)*_C1*a-b))^(1/2),_a = y(x))-x-_C2 = 0, Intat(-a/(a*(exp(
-_a^2*a)*_C1*a-b))^(1/2),_a = y(x))-x-_C2 = 0