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 = 0.225282 (sec), leaf count = 34
\[\left \{\left \{y(x)\to -\frac {x}{\sqrt {-1+c_1 x}}\right \},\left \{y(x)\to \frac {x}{\sqrt {-1+c_1 x}}\right \}\right \}\]
Maple ✓
cpu = 0.015 (sec), leaf count = 26
\[\left [y \left (x \right ) = \frac {x}{\sqrt {x \textit {\_C1} -1}}, y \left (x \right ) = -\frac {x}{\sqrt {x \textit {\_C1} -1}}\right ]\] 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))
Maple raw output
[y(x) = 1/(_C1*x-1)^(1/2)*x, y(x) = -1/(_C1*x-1)^(1/2)*x]