ODE No. 451

\[ \left (a+x^2\right ) y'(x)^2+b-2 x y(x) y'(x)+y(x)^2=0 \] Mathematica : cpu = 0.0494847 (sec), leaf count = 51

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

\[\left \{\left \{y(x)\to c_1 x-\sqrt {-b-a c_1{}^2}\right \},\left \{y(x)\to \sqrt {-b-a c_1{}^2}+c_1 x\right \}\right \}\] Maple : cpu = 0.066 (sec), leaf count = 78

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

\[y \left (x \right ) = \frac {\sqrt {-a b \left (x^{2}+a \right )}}{a}\]