ODE No. 452

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

✓ Mathematica : cpu = 0.0173581 (sec), leaf count = 23

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

\[\left \{\left \{y(x)\to \frac {-c_1 x+1+c_1{}^2}{x+c_1}\right \}\right \}\]

✗ Maple : cpu = 0. (sec), leaf count = 0

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

, could not solve

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