ODE No. 570

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

\[ \left (y'(x)^2+1\right ) \left (a x+\tan ^{-1}\left (y'(x)\right )\right )+y'(x)=0 \] Mathematica : cpu = 0.112349 (sec), leaf count = 0 , could not solve

DSolve[Derivative[1][y][x] + (a*x + ArcTan[Derivative[1][y][x]])*(1 + Derivative[1][y][x]^2) == 0, y[x], x]

Maple : cpu = 0.062 (sec), leaf count = 30

\[ \left \{ y \left ( x \right ) =\int \!\tan \left ( {\it RootOf} \left ( ax \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+ \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{\it \_Z}+ax+\tan \left ( {\it \_Z} \right ) +{\it \_Z} \right ) \right ) \,{\rm d}x+{\it \_C1} \right \} \]