ODE
\[ \left (1-x^2 y(x)^2\right ) y'(x)=x y(x)^3 \] ODE Classification
[[_homogeneous, `class G`], _rational]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 0.316315 (sec), leaf count = 55
\[\left \{\left \{y(x)\to -\frac {i \sqrt {W\left (-e^{-2 c_1} x^2\right )}}{x}\right \},\left \{y(x)\to \frac {i \sqrt {W\left (-e^{-2 c_1} x^2\right )}}{x}\right \}\right \}\]
Maple ✓
cpu = 0.378 (sec), leaf count = 21
\[\left [y \left (x \right ) = {\mathrm e}^{-\frac {\LambertW \left (-x^{2} {\mathrm e}^{-2 \textit {\_C1}}\right )}{2}-\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[(1 - x^2*y[x]^2)*y'[x] == x*y[x]^3,y[x],x]
Mathematica raw output
{{y[x] -> ((-I)*Sqrt[ProductLog[-(x^2/E^(2*C[1]))]])/x}, {y[x] -> (I*Sqrt[ProductLog[-(x^2/E^(2*C[1]))]])/x}}
Maple raw input
dsolve((1-x^2*y(x)^2)*diff(y(x),x) = x*y(x)^3, y(x))
Maple raw output
[y(x) = exp(-1/2*LambertW(-x^2*exp(-2*_C1))-_C1)]