##### 4.12.5 $$2 x \left (2 x^2+y(x)\right ) y'(x)+y(x) \left (12 x^2+y(x)\right )=0$$

ODE
$2 x \left (2 x^2+y(x)\right ) y'(x)+y(x) \left (12 x^2+y(x)\right )=0$ ODE Classiﬁcation

[[_homogeneous, class G], _exact, _rational, [_Abel, 2nd type, class B]]

Book solution method
Exact equation

Mathematica
cpu = 0.373363 (sec), leaf count = 58

$\left \{\left \{y(x)\to -\frac {2 x^3+\sqrt {x \left (4 x^5+c_1\right )}}{x}\right \},\left \{y(x)\to \frac {-2 x^3+\sqrt {x \left (4 x^5+c_1\right )}}{x}\right \}\right \}$

Maple
cpu = 0.19 (sec), leaf count = 50

$\left [y \left (x \right ) = \frac {-2 x^{3}+\sqrt {4 x^{6}+x \textit {\_C1}}}{x}, y \left (x \right ) = -\frac {2 x^{3}+\sqrt {4 x^{6}+x \textit {\_C1}}}{x}\right ]$ Mathematica raw input

DSolve[y[x]*(12*x^2 + y[x]) + 2*x*(2*x^2 + y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -((2*x^3 + Sqrt[x*(4*x^5 + C[1])])/x)}, {y[x] -> (-2*x^3 + Sqrt[x*(4*x
^5 + C[1])])/x}}

Maple raw input

dsolve(2*x*(2*x^2+y(x))*diff(y(x),x)+(12*x^2+y(x))*y(x) = 0, y(x))

Maple raw output

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