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 = 0.342816 (sec), leaf count = 55

\[\left \{\left \{y(x)\to c_2 \exp \left (\frac {\sqrt {b^2-x^2}}{a}+\frac {c_1 \log \left (a \sqrt {b^2-x^2}-c_1\right )}{a^2}\right )\right \}\right \}\] Maple : cpu = 2.704 (sec), leaf count = 50

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