\[ \boxed { \left ( \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+1 \right ) \left ( \arctan \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) +ax \right ) +{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.108514 (sec), leaf count = 29 \[ \text {DSolve}\left [\left (y'(x)^2+1\right ) \left (a x+\tan ^{-1}\left (y'(x)\right )\right )+y'(x)=0,y(x),x\right ] \]
Maple: cpu = 0.047 (sec), leaf count = 30 \[ \left \{ y \left ( x \right ) =\int \!\tan \left ( {\it RootOf} \left ( ax \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+ \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{\it \_Z}+ax+\tan \left ( {\it \_Z} \right ) +{\it \_Z} \right ) \right ) \,{\rm d}x+{\it \_C1} \right \} \]