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

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

[`y=_G(x,y')`]

Book solution method
Change of variable

Mathematica
cpu = 600.27 (sec), leaf count = 0 , timed out

$Aborted

Maple
cpu = 1.707 (sec), leaf count = 17

\[ \left \{ \left (y \relax (x ) \right ) ^{2}+6\,xy \relax (x ) +{x}^{2}-4=0 \right \} \] Mathematica raw input

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

Mathematica raw output

$Aborted

Maple raw input

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

Maple raw output

y(x)^2+6*x*y(x)+x^2-4 = 0