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 = 0.168798 (sec), leaf count = 23
\[\left \{\left \{y(x)\to \frac {-c_1 x+1+c_1{}^2}{x+c_1}\right \}\right \}\]
Maple ✗
cpu = 1.723 (sec), leaf count = 0 , could not solve
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))
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
{{y[x] -> (1 - x*C[1] + C[1]^2)/(x + C[1])}}
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))
Maple raw output
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))