\[ y''(x)=-\frac {y'(x) (-\text {cn}(x|k) \text {dn}(x|k)-2 \text {sn}(x|k))}{\text {sn}(x|k)^2-\text {sn}(a|k)^2}-\frac {y(x) \left (6 k^2 \text {sn}(a|k)^4-4 \left (k^2+1\right ) \text {sn}(a|k)^2+2\right )}{\text {sn}(x|k)^2-\text {sn}(a|k)^2}-\frac {1}{\text {sn}(x|k)^2-\text {sn}(a|k)^2} \] ✗ Mathematica : cpu = 1.76096 (sec), leaf count = 0 , could not solve
DSolve[Derivative[2][y][x] == -(-JacobiSN[a, k]^2 + JacobiSN[x, k]^2)^(-1) - ((2 - 4*(1 + k^2)*JacobiSN[a, k]^2 + 6*k^2*JacobiSN[a, k]^4)*y[x])/(-JacobiSN[a, k]^2 + JacobiSN[x, k]^2) - ((-(JacobiCN[x, k]*JacobiDN[x, k]) - 2*JacobiSN[x, k])*Derivative[1][y][x])/(-JacobiSN[a, k]^2 + JacobiSN[x, k]^2), y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol
\[\left \{y \left (x \right ) = \mathit {DESol}\left (\left \{-\frac {2 \left (\frac {d}{d x}\textit {\_Y} \left (x \right )\right ) \mathrm {cn}\left (x | k \right ) \mathrm {dn}\left (x | k \right ) \mathrm {sn}\left (x | k \right )}{\mathrm {sn}\left (x | k \right )^{2}-\mathrm {sn}\left (a | k \right )}-\frac {\left (-6 k^{2} \mathrm {sn}\left (a | k \right )^{4}+4 \left (k^{2}+1\right ) \mathrm {sn}\left (a | k \right )^{2}-2\right ) \textit {\_Y} \left (x \right )}{\mathrm {sn}\left (x | k \right )^{2}-\mathrm {sn}\left (a | k \right )}+\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\right \}\]