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 = 0.00902352 (sec), leaf count = 44

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

Maple
cpu = 0.005 (sec), leaf count = 19

\[ \left \{ {\frac {a}{{x}^{2}}}-{\frac {{\it \_C1}}{{x}^{3}}}+ \left (y \relax (x ) \right ) ^{-2}=0 \right \} \] 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),'implicit')

Maple raw output

a/x^2-1/x^3*_C1+1/y(x)^2 = 0