\[ \boxed { {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) - \left ( 3\,{k}^{2} \left ( {\it JacobiSN} \left ( z,x \right ) \right ) ^{2}+a \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( b+c \left ( {\it JacobiSN} \left ( z,x \right ) \right ) ^{2}-3\,{k}^{2}{\it JacobiSN} \left ( z,x \right ) {\it JacobiCN} \left ( z,x \right ) {\it JacobiDN} \left ( z,x \right ) \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.029504 (sec), leaf count = 55 \[ \text {DSolve}\left [-y'(x) \left (a+3 k^2 \text {sn}(z|x)^2\right )+y(x) \left (b+c \text {sn}(z|x)^2-3 k^2 \text {cn}(z|x) \text {dn}(z|x) \text {sn}(z|x)\right )+y^{(3)}(x)=0,y(x),x\right ] \]
Maple: cpu = 1.154 (sec), leaf count = 63 \[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac { {\rm d}^{3}}{{\rm d}{x}^{3}}}{\it \_Y} \left ( x \right ) + \left ( -3\,{ k}^{2} \left ( {\it JacobiSN} \left ( z,x \right ) \right ) ^{2}-a \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) + \left ( b+c \left ( {\it JacobiSN} \left ( z,x \right ) \right ) ^{2}-3\,{k}^{2}{ \it JacobiSN} \left ( z,x \right ) {\it JacobiCN} \left ( z,x \right ) { \it JacobiDN} \left ( z,x \right ) \right ) {\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]