\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) ={\frac {2\,{\it JacobiSN} \left ( x,k \right ) {\it JacobiCN} \left ( x,k \right ) {\it JacobiDN} \left ( x,k \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\, \left ( 1-2\, \left ( {k}^{2}+1 \right ) \left ( {\it JacobiSN} \left ( a,k \right ) \right ) ^{2}+3\,{k}^{2} \left ( {\it JacobiSN} \left ( a,k \right ) \right ) ^{4} \right ) y \left ( x \right ) }{ \left ( {\it JacobiSN} \left ( x,k \right ) \right ) ^{2}-{\it JacobiSN} \left ( a,k \right ) }}=0} \]
Mathematica: cpu = 1.467186 (sec), leaf count = 105 \[ \text {DSolve}\left [y''(x)=-\frac {y'(x) (-\text {cn}(x|k) \text {dn}(x|k)-2 \text {sn}(x|k))}{\text {sn}(x|k)^2-\text {sn}(a|k)^2}-\frac {y(x) \left (6 k^2 \text {sn}(a|k)^4-4 \left (k^2+1\right ) \text {sn}(a|k)^2+2\right )}{\text {sn}(x|k)^2-\text {sn}(a|k)^2}-\frac {1}{\text {sn}(x|k)^2-\text {sn}(a|k)^2},y(x),x\right ] \]
Maple: cpu = 340.784 (sec), leaf count = 85 \[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac { {\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) -2\,{\frac {{ \it JacobiSN} \left ( x,k \right ) {\it JacobiCN} \left ( x,k \right ) { \it JacobiDN} \left ( x,k \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) }{ \left ( {\it JacobiSN} \left ( x,k \right ) \right ) ^{2}-{\it JacobiSN} \left ( a,k \right ) }}-{\frac { \left ( -2+ 4\, \left ( {k}^{2}+1 \right ) \left ( {\it JacobiSN} \left ( a,k \right ) \right ) ^{2}-6\,{k}^{2} \left ( {\it JacobiSN} \left ( a,k \right ) \right ) ^{4} \right ) {\it \_Y} \left ( x \right ) }{ \left ( { \it JacobiSN} \left ( x,k \right ) \right ) ^{2}-{\it JacobiSN} \left ( a ,k \right ) }} \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]