2.191   ODE No. 191

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

\[ \sqrt {1-x^2} y'(x)-y(x) \sqrt {y(x)^2-1}=0 \] Mathematica : cpu = 0.0292108 (sec), leaf count = 48

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

Maple : cpu = 0.017 (sec), leaf count = 16

\[ \left \{ \arcsin \left ( x \right ) +\arctan \left ( {\frac {1}{\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-1}}} \right ) +{\it \_C1}=0 \right \} \]