\[ \boxed { {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) +f \left ( x \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +g \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( f \left ( x \right ) g \left ( x \right ) +{\frac {\rm d}{{\rm d}x}}g \left ( x \right ) \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.012002 (sec), leaf count = 38 \[ \text {DSolve}\left [y(x) \left (f(x) g(x)+g'(x)\right )+f(x) y''(x)+g(x) y'(x)+y^{(3)}(x)=0,y(x),x\right ] \]
Maple: cpu = 0.046 (sec), leaf count = 47 \[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac { {\rm d}^{3}}{{\rm d}{x}^{3}}}{\it \_Y} \left ( x \right ) +f \left ( x \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) +g \left ( x \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) + \left ( f \left ( x \right ) g \left ( x \right ) +{ \frac {\rm d}{{\rm d}x}}g \left ( x \right ) \right ) {\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]