2.456   ODE No. 456

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

✓ Mathematica : cpu = 1.3023 (sec), leaf count = 473

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

\[\left \{\left \{y(x)\to \frac {x \left (1+\tanh ^2\left (\frac {1}{2} \left (c_1-2 \tanh ^{-1}\left (\frac {-i \sqrt {x+1} \sqrt {x-1}+i \sqrt {3} \sqrt {x-1}+i \sqrt {x+1}-i \sqrt {3}}{-2 x+\sqrt {x-1} \left (\sqrt {3} \sqrt {x+1}-1\right )+\sqrt {3} \sqrt {x+1}-1}\right )\right )\right )\right )}{-1+\tanh ^2\left (\frac {1}{2} \left (c_1-2 \tanh ^{-1}\left (\frac {-i \sqrt {x+1} \sqrt {x-1}+i \sqrt {3} \sqrt {x-1}+i \sqrt {x+1}-i \sqrt {3}}{-2 x+\sqrt {x-1} \left (\sqrt {3} \sqrt {x+1}-1\right )+\sqrt {3} \sqrt {x+1}-1}\right )\right )\right )}\right \},\left \{y(x)\to \frac {x \left (1+\tanh ^2\left (\frac {1}{2} \left (2 \tanh ^{-1}\left (\frac {-i \sqrt {x+1} \sqrt {x-1}+i \sqrt {3} \sqrt {x-1}+i \sqrt {x+1}-i \sqrt {3}}{-2 x+\sqrt {x-1} \left (\sqrt {3} \sqrt {x+1}-1\right )+\sqrt {3} \sqrt {x+1}-1}\right )+c_1\right )\right )\right )}{-1+\tanh ^2\left (\frac {1}{2} \left (2 \tanh ^{-1}\left (\frac {-i \sqrt {x+1} \sqrt {x-1}+i \sqrt {3} \sqrt {x-1}+i \sqrt {x+1}-i \sqrt {3}}{-2 x+\sqrt {x-1} \left (\sqrt {3} \sqrt {x+1}-1\right )+\sqrt {3} \sqrt {x+1}-1}\right )+c_1\right )\right )}\right \}\right \}\]

✓ Maple : cpu = 0.534 (sec), leaf count = 33

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

\[y \left (x \right ) = x\]