\[ \boxed { {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) + \left ( -{n}^{2}+1 \right ) {\it WeierstrassP} \left ( x,{\it g2},{\it g3} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +1/2\, \left ( \left ( -{n}^{2}+1 \right ) {\it WeierstrassPPrime} \left ( x,{\it g2},{\it g3} \right ) -a \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.018502 (sec), leaf count = 51 \[ \text {DSolve}\left [\frac {1}{2} y(x) \left (\left (1-n^2\right ) \wp '(x;\text {g2},\text {g3})-a\right )+\left (1-n^2\right ) y'(x) \wp (x;\text {g2},\text {g3})+y^{(3)}(x)=0,y(x),x\right ] \]
Maple: cpu = 0.218 (sec), leaf count = 59 \[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac { {\rm d}^{3}}{{\rm d}{x}^{3}}}{\it \_Y} \left ( x \right ) + \left ( -{n}^ {2}{\it WeierstrassP} \left ( x,{\it g2},{\it g3} \right ) +{\it WeierstrassP} \left ( x,{\it g2},{\it g3} \right ) \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) + \left ( -{\frac {{\it WeierstrassPPrime} \left ( x,{\it g2},{\it g3} \right ) {n}^{2}}{2}}+{ \frac {{\it WeierstrassPPrime} \left ( x,{\it g2},{\it g3} \right ) }{2} }-{\frac {a}{2}} \right ) {\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]