4.1018   9 (1− x2)y(x)4y′(x)2 + 4x2 + 6xy(x)5y′(x) = 0

ODE

9(1− x2)y(x)4y′(x)2 + 4x2 + 6xy(x)5y′(x) = 0

ODE Classification

[[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

Book solution method
Change of variable

Mathematica
cpu = 616.913 (sec), leaf count = 0 , timed out

$Aborted

Maple
cpu = 2.7 (sec), leaf count = 62

{                ∘ ---------------                   ∘ ---------------                      }
              3         6    2                    3         6     2             6    2
 − C1 − (y(x)) +   (y (x )) + 4x − 4 = 0,−-C1 + (y (x )) +   (y(x)) + 4x − 4 = 0,(y(x)) + 4x − 4 = 0

Mathematica raw input

DSolve[4*x^2 + 6*x*y[x]^5*y'[x] + 9*(1 - x^2)*y[x]^4*y'[x]^2 == 0,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve(9*(-x^2+1)*y(x)^4*diff(y(x),x)^2+6*x*y(x)^5*diff(y(x),x)+4*x^2 = 0, y(x),'implicit')

Maple raw output

y(x)^6+4*x^2-4 = 0, -_C1+y(x)^3+(y(x)^6+4*x^2-4)^(1/2) = 0, -_C1-y(x)^3+(y(x)^6+
4*x^2-4)^(1/2) = 0