4.602   (x2 + y(x)2) y′(x) = xy(x)

ODE

(x2 + y(x)2)y′(x) = xy(x)

ODE Classification

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

Book solution method
Homogeneous equation

Mathematica
cpu = 1.37322 (sec), leaf count = 44

{{                     }  {                   } }
                x                       x
   y(x) → − ∘-----−2c1-2-- , y(x) → ∘-----−2c1-2-
             W (e   x )             W (e    x)

Maple
cpu = 0.015 (sec), leaf count = 29

{    (     )      2                   }
 − ln  y-(x-) + ---x---2 − ln(x)− -C1 = 0
        x     2 (y (x))

Mathematica raw input

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

Mathematica raw output

{{y[x] -> -(x/Sqrt[ProductLog[x^2/E^(2*C[1])]])}, {y[x] -> x/Sqrt[ProductLog[x^2
/E^(2*C[1])]]}}

Maple raw input

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

Maple raw output

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