4.14.16 \(\left (1-x^2 y(x)^2\right ) y'(x)=x y(x)^3\)

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 = 0.021548 (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 = 0.011 (sec), leaf count = 25

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

Maple raw output

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