4.8.19 $$2 x^3 y'(x)=y(x) \left (a y(x)^2+3 x^2\right )$$

ODE
$2 x^3 y'(x)=y(x) \left (a y(x)^2+3 x^2\right )$ ODE Classiﬁcation

[[_homogeneous, class A], _rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.234256 (sec), leaf count = 44

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

Maple
cpu = 0.019 (sec), leaf count = 48

$\left [y \left (x \right ) = \frac {\sqrt {\left (-a x +\textit {\_C1} \right ) x}\, x}{-a x +\textit {\_C1}}, y \left (x \right ) = -\frac {\sqrt {\left (-a x +\textit {\_C1} \right ) x}\, x}{-a x +\textit {\_C1}}\right ]$ Mathematica raw input

DSolve[2*x^3*y'[x] == y[x]*(3*x^2 + a*y[x]^2),y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(2*x^3*diff(y(x),x) = (3*x^2+a*y(x)^2)*y(x), y(x))

Maple raw output

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