2.451   ODE No. 451

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ \left (a+x^2\right ) y'(x)^2+b-2 x y(x) y'(x)+y(x)^2=0 \] Mathematica : cpu = 0.056729 (sec), leaf count = 51

\[\left \{\left \{y(x)\to c_1 x-\sqrt {-b-a c_1{}^2}\right \},\left \{y(x)\to \sqrt {-b-a c_1{}^2}+c_1 x\right \}\right \}\] Maple : cpu = 0.065 (sec), leaf count = 78

\[\left \{y \left (x \right ) = \frac {\sqrt {-\left (x^{2}+a \right ) a b}}{a}, y \left (x \right ) = -\frac {\sqrt {-\left (x^{2}+a \right ) a b}}{a}, y \left (x \right ) = c_{1} x -\sqrt {-a c_{1}^{2}-b}, y \left (x \right ) = c_{1} x +\sqrt {-a c_{1}^{2}-b}\right \}\]