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

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

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

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.00889937 (sec), leaf count = 46

\[\left \{\left \{y(x)\to -\frac {x^2}{\sqrt {c_1+\frac {4 x^3}{3}}}\right \},\left \{y(x)\to \frac {x^2}{\sqrt {c_1+\frac {4 x^3}{3}}}\right \}\right \}\]

Maple
cpu = 0.006 (sec), leaf count = 19

\[ \left \{ \left (y \relax (x ) \right ) ^{-2}-{\frac {4}{3\,x}}-{\frac {{\it \_C1}}{{x}^{4}}}=0 \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> -(x^2/Sqrt[(4*x^3)/3 + C[1]])}, {y[x] -> x^2/Sqrt[(4*x^3)/3 + C[1]]}}

Maple raw input

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

Maple raw output

1/y(x)^2-4/3/x-1/x^4*_C1 = 0