ODE No. 495

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

\[ \left ((1-a) x^2+y(x)^2\right ) y'(x)^2+2 a x y(x) y'(x)+(1-a) y(x)^2+x^2=0 \] Mathematica : cpu = 0.148599 (sec), leaf count = 83

\[\left \{\text {Solve}\left [\sqrt {a-1} \tan ^{-1}\left (\frac {y(x)}{x}\right )-\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )=c_1+\log (x),y(x)\right ],\text {Solve}\left [\sqrt {a-1} \tan ^{-1}\left (\frac {y(x)}{x}\right )+\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )=c_1-\log (x),y(x)\right ]\right \}\] Maple : cpu = 11.317 (sec), leaf count = 61

\[ \left \{ y \left ( x \right ) =\tan \left ( {\it RootOf} \left ( -2\,{\it \_Z}\,\sqrt {a-1}-\ln \left ( {\frac {{x}^{2}}{ \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2}}} \right ) +2\,{\it \_C1} \right ) \right ) x,y \left ( x \right ) =\tan \left ( {\it RootOf} \left ( 2\,{\it \_Z}\,\sqrt {a-1}-\ln \left ( {\frac {{x}^{2}}{ \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2}}} \right ) +2\,{\it \_C1} \right ) \right ) x \right \} \]