4.14.26 \(y(x) \left (x^2 y(x)^2+1\right )+x (1-x y(x))^2 y'(x)=0\)

ODE
\[ y(x) \left (x^2 y(x)^2+1\right )+x (1-x y(x))^2 y'(x)=0 \] ODE Classification

[[_homogeneous, `class G`], _rational]

Book solution method
Homogeneous equation, isobaric equation

Mathematica
cpu = 0.066161 (sec), leaf count = 24

\[\text {Solve}\left [c_1+\frac {1}{x y(x)}+2 \log (y(x))=x y(x),y(x)\right ]\]

Maple
cpu = 0.018 (sec), leaf count = 43

\[ \left \{ {\frac {-2\,\ln \left (xy \relax (x ) \right ) xy \relax (x ) -1+{x}^{2} \left (y \relax (x ) \right ) ^{2}-2\,x \left ({\it \_C1}-\ln \relax (x ) \right ) y \relax (x ) }{2\,xy \relax (x ) }}=0 \right \} \] Mathematica raw input

DSolve[y[x]*(1 + x^2*y[x]^2) + x*(1 - x*y[x])^2*y'[x] == 0,y[x],x]

Mathematica raw output

Solve[C[1] + 2*Log[y[x]] + 1/(x*y[x]) == x*y[x], y[x]]

Maple raw input

dsolve(x*(1-x*y(x))^2*diff(y(x),x)+(1+x^2*y(x)^2)*y(x) = 0, y(x),'implicit')

Maple raw output

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