\[ -y'(x) \left (a+6 k^2 \sin ^2(x)\right )+b y(x)+y^{(3)}(x)=0 \] ✗ Mathematica : cpu = 0.0161775 (sec), leaf count = 0 , could not solve
DSolve[b*y[x] - (a + 6*k^2*Sin[x]^2)*Derivative[1][y][x] + Derivative[3][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol
\[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}{\it \_Y} \left ( x \right ) + \left ( -6\,{k}^{2} \left ( \sin \left ( x \right ) \right ) ^{2}-a \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) +b{\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]