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 = 0.224418 (sec), leaf count = 42

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

Maple
cpu = 0.029 (sec), leaf count = 67

\[ \left \{ \left (y \relax (x ) \right ) ^{-1}+3\,{\frac {x\ln \left (x+\sqrt {{x}^{2}-1} \right ) }{\sqrt {{x}^{2}-1}}}-3-3\,{\frac {\ln \left (x+\sqrt {{x}^{2}-1} \right ) }{\sqrt {{x}^{2}-1}x}}-{\frac {{\it \_C1}}{x}\sqrt {-1+x}\sqrt {1+x}}=0 \right \} \] 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),'implicit')

Maple raw output

1/y(x)+3*x/(x^2-1)^(1/2)*ln(x+(x^2-1)^(1/2))-3-3/x/(x^2-1)^(1/2)*ln(x+(x^2-1)^(1
/2))-(-1+x)^(1/2)*(1+x)^(1/2)/x*_C1 = 0