\[ y''(x)=-\frac {y'(x) (-\text {cn}(x|k) \text {dn}(x|k)-2 \text {sn}(x|k))}{\text {sn}(x|k)^2-\text {sn}(a|k)^2}-\frac {y(x) \left (6 k^2 \text {sn}(a|k)^4-4 \left (k^2+1\right ) \text {sn}(a|k)^2+2\right )}{\text {sn}(x|k)^2-\text {sn}(a|k)^2}-\frac {1}{\text {sn}(x|k)^2-\text {sn}(a|k)^2} \] ✗ Mathematica : cpu = 1.11897 (sec), leaf count = 0
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]
, 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
dsolve(diff(diff(y(x),x),x) = (2*JacobiSN(x,k)*JacobiCN(x,k)*JacobiDN(x,k)*diff(y(x),x)-2*(1-2*(k^2+1)*JacobiSN(a,k)^2+3*k^2*JacobiSN(a,k)^4)*y(x))/(JacobiSN(x,k)^2-JacobiSN(a,k)),y(x))
, result contains DESol or ODESolStruc
\[y \left (x \right ) = \mathit {DESol}\left (\left \{\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )-\frac {2 \,\mathrm {sn}\left (x | k \right ) \mathrm {cn}\left (x | k \right ) \mathrm {dn}\left (x | k \right ) \left (\frac {d}{d x}\textit {\_Y} \left (x \right )\right )}{\mathrm {sn}\left (x | k \right )^{2}-\mathrm {sn}\left (a | k \right )}-\frac {\left (-2+4 \left (k^{2}+1\right ) \mathrm {sn}\left (a | k \right )^{2}-6 k^{2} \mathrm {sn}\left (a | k \right )^{4}\right ) \textit {\_Y} \left (x \right )}{\mathrm {sn}\left (x | k \right )^{2}-\mathrm {sn}\left (a | k \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\]