2.431   ODE No. 431

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

\[ x^2 y'(x)^2-y(x)^4+y(x)^2=0 \] Mathematica : cpu = 0.058878 (sec), leaf count = 81

\[\left \{\left \{y(x)\to -\sqrt {1+\tan ^2(-\log (x)+c_1)}\right \},\left \{y(x)\to \sqrt {1+\tan ^2(-\log (x)+c_1)}\right \},\left \{y(x)\to -\sqrt {1+\tan ^2(\log (x)+c_1)}\right \},\left \{y(x)\to \sqrt {1+\tan ^2(\log (x)+c_1)}\right \}\right \}\] Maple : cpu = 0.208 (sec), leaf count = 62

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