4.14.17 \(\left (1-x^2 y(x)^2\right ) y'(x)=y(x)^2 (x y(x)+1)\)

ODE
\[ \left (1-x^2 y(x)^2\right ) y'(x)=y(x)^2 (x y(x)+1) \] ODE Classification

[[_homogeneous, `class G`], _rational, [_Abel, `2nd type``class B`]]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.0385589 (sec), leaf count = 29

\[\left \{\left \{y(x)\to -\frac {1}{x}\right \},\left \{y(x)\to -\frac {W\left (-e^{-c_1} x\right )}{x}\right \}\right \}\]

Maple
cpu = 0.025 (sec), leaf count = 27

\[ \left \{ x+{\frac {-\ln \left (y \relax (x ) \right ) -{\it \_C1}}{y \relax (x ) }}=0,y \relax (x ) =-{x}^{-1} \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> -x^(-1)}, {y[x] -> -(ProductLog[-(x/E^C[1])]/x)}}

Maple raw input

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

Maple raw output

y(x) = -1/x, x+(-ln(y(x))-_C1)/y(x) = 0