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]