4.915   x2y′(x)2 + (y(x)+ 2x)y(x)y′(x)+ y(x)2 = 0

ODE

x2y′(x )2 +(y(x)+ 2x)y(x)y′(x)+ y(x)2 = 0

ODE Classification

[[_homogeneous, `class A`], _dAlembert]

Book solution method
Change of variable

Mathematica
cpu = 0.131129 (sec), leaf count = 64

{ {                              }  {                             }}
           --sinh-(4c1)+-cosh(4c1)-           --sinh(4c1)+-cosh-(4c1)--
   y(x) → −sinh(2c1) + cosh(2c1)− x  , y(x) → sinh (2c1)+ cosh(2c1) + x

Maple
cpu = 0.08 (sec), leaf count = 99

{           (  ( ∘ ---------------           ))       (    )                     (  ( ∘ ---------------           ))       (     )                    }
 ln(x)− 1 ln  -1    y(x)(y(x)+-4x)x+ 2x + y(x)   + 1 ln  y-(x)  − -C1 = 0,ln(x)+  1ln  1-   y(x)(y(x)+-4x)x + 2x+ y(x)   + 1 ln  y-(x) − -C1 = 0,y(x) = − 4x
        2    x           x2                       2      x                    2    x          x2                       2      x

Mathematica raw input

DSolve[y[x]^2 + y[x]*(2*x + y[x])*y'[x] + x^2*y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> -((Cosh[4*C[1]] + Sinh[4*C[1]])/(-x + Cosh[2*C[1]] + Sinh[2*C[1]]))}, 
{y[x] -> (Cosh[4*C[1]] + Sinh[4*C[1]])/(x + Cosh[2*C[1]] + Sinh[2*C[1]])}}

Maple raw input

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

Maple raw output

y(x) = -4*x, ln(x)-1/2*ln(((y(x)*(y(x)+4*x)/x^2)^(1/2)*x+2*x+y(x))/x)+1/2*ln(y(x
)/x)-_C1 = 0, ln(x)+1/2*ln(((y(x)*(y(x)+4*x)/x^2)^(1/2)*x+2*x+y(x))/x)+1/2*ln(y(
x)/x)-_C1 = 0