2.1767   ODE No. 1767

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

\[ \left (\frac {a x}{\sqrt {b^2-x^2}}-x\right ) y'(x)^2+x y(x) y''(x)-y(x) y'(x)=0 \] Mathematica : cpu = 0.0759833 (sec), leaf count = 54

\[\left \{\left \{y(x)\to c_2 e^{\frac {\sqrt {b^2-x^2}}{a}} \left (a \sqrt {b^2-x^2}-c_1\right ){}^{\frac {c_1}{a^2}}\right \}\right \}\]

Maple : cpu = 0.345 (sec), leaf count = 50

\[ \left \{ y \left ( x \right ) ={\it \_C2}\,{{\rm e}^{\int \!-{x\sqrt {{b}^{2}-{x}^{2}} \left ( {\it \_C1}\,\sqrt {{b}^{2}-{x}^{2}}+a \left ( {b}^{2}-{x}^{2} \right ) \right ) ^{-1}}\,{\rm d}x}} \right \} \]