##### 4.8.28 $$x^2 \left (1-x^2\right ) y'(x)=y(x) \left (x-3 x^3 y(x)\right )$$

ODE
$x^2 \left (1-x^2\right ) y'(x)=y(x) \left (x-3 x^3 y(x)\right )$ ODE Classiﬁcation

[_rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.277016 (sec), leaf count = 42

$\left \{\left \{y(x)\to \frac {x}{-3 \sqrt {1-x^2} \sin ^{-1}(x)+c_1 \sqrt {1-x^2}+3 x}\right \}\right \}$

Maple
cpu = 0.051 (sec), leaf count = 72

$\left [y \left (x \right ) = \frac {\sqrt {x^{2}-1}\, x}{\sqrt {x -1}\, \sqrt {1+x}\, \textit {\_C1} \sqrt {x^{2}-1}-3 \ln \left (x +\sqrt {x^{2}-1}\right ) x^{2}+3 \sqrt {x^{2}-1}\, x +3 \ln \left (x +\sqrt {x^{2}-1}\right )}\right ]$ Mathematica raw input

DSolve[x^2*(1 - x^2)*y'[x] == y[x]*(x - 3*x^3*y[x]),y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(x^2*(-x^2+1)*diff(y(x),x) = (x-3*x^3*y(x))*y(x), y(x))

Maple raw output

[y(x) = (x^2-1)^(1/2)*x/((x-1)^(1/2)*(1+x)^(1/2)*_C1*(x^2-1)^(1/2)-3*ln(x+(x^2-1
)^(1/2))*x^2+3*(x^2-1)^(1/2)*x+3*ln(x+(x^2-1)^(1/2)))]