4.8.18 \(2 x^3 y'(x)=y(x) \left (x^2-y(x)^2\right )\)

ODE
\[ 2 x^3 y'(x)=y(x) \left (x^2-y(x)^2\right ) \] ODE Classification

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

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.137588 (sec), leaf count = 34

\[\left \{\left \{y(x)\to -\frac {x}{\sqrt {c_1 x-1}}\right \},\left \{y(x)\to \frac {x}{\sqrt {c_1 x-1}}\right \}\right \}\]

Maple
cpu = 0.005 (sec), leaf count = 17

\[ \left \{ {x}^{-2}-{\frac {{\it \_C1}}{x}}+ \left (y \relax (x ) \right ) ^{-2}=0 \right \} \] Mathematica raw input

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

Mathematica raw output

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

Maple raw input

dsolve(2*x^3*diff(y(x),x) = (x^2-y(x)^2)*y(x), y(x),'implicit')

Maple raw output

1/x^2-1/x*_C1+1/y(x)^2 = 0