2.637   ODE No. 637

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

\[ y'(x)=\frac {e^{-x^2} x}{e^{x^2} y(x)+1} \] Mathematica : cpu = 15.6765 (sec), leaf count = 53

\[\text {Solve}\left [2 x^2=4 c_1+\log \left (2 e^{2 x^2} y(x)^2+2 e^{x^2} y(x)+1\right )+2 \tan ^{-1}\left (2 e^{x^2} y(x)+1\right ),y(x)\right ]\]

Maple : cpu = 27.176 (sec), leaf count = 84

\[ \left \{ y \left ( x \right ) =-{\frac {1}{{{\rm e}^{{x}^{2}}}}\tan \left ( {\it RootOf} \left ( 2\,{x}^{2}-\ln \left ( {\frac {81\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}}{10}}+{\frac {81}{10}} \right ) +2\,\ln \left ( 9/2\,\tan \left ( {\it \_Z} \right ) -9/2 \right ) +6\,{\it \_C1}-2\,{\it \_Z} \right ) \right ) \left ( \tan \left ( {\it RootOf} \left ( 2\,{x}^{2}-\ln \left ( {\frac {81\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}}{10}}+{\frac {81}{10}} \right ) +2\,\ln \left ( 9/2\,\tan \left ( {\it \_Z} \right ) -9/2 \right ) +6\,{\it \_C1}-2\,{\it \_Z} \right ) \right ) -1 \right ) ^{-1}} \right \} \]