ODE No. 446

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

✓ Mathematica : cpu = 0.0402572 (sec), leaf count = 45

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

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

✓ Maple : cpu = 0.043 (sec), leaf count = 57

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

\[y \left (x \right ) = \sqrt {x^{2}+1}\]