\[ \boxed { {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) - \left ( 6\,{k}^{2} \left ( \sin \left ( x \right ) \right ) ^{2}+a \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +by \left ( x \right ) =0} \]
Mathematica: cpu = 0.022003 (sec), leaf count = 32 \[ \text {DSolve}\left [-y'(x) \left (a+6 k^2 \sin ^2(x)\right )+b y(x)+y^{(3)}(x)=0,y(x),x\right ] \]
Maple: cpu = 1.264 (sec), leaf count = 40 \[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac { {\rm d}^{3}}{{\rm d}{x}^{3}}}{\it \_Y} \left ( x \right ) + \left ( -6\,{ k}^{2} \left ( \sin \left ( x \right ) \right ) ^{2}-a \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) +b{\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]