\[ -y''(x) \left (a+12 k^2 \text {sn}(z|x)^2\right )+y(x) \left (\alpha \text {sn}(z|x)^2+\beta \right )+b y'(x)+y^{(4)}(x)=0 \] ✗ Mathematica : cpu = 0.0814704 (sec), leaf count = 0 , could not solve
DSolve[(beta + alpha*JacobiSN[z, x]^2)*y[x] + b*Derivative[1][y][x] - (a + 12*k^2*JacobiSN[z, x]^2)*Derivative[2][y][x] + Derivative[4][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol
\[\{y \left (x \right ) = \mathit {DESol}\left (\left \{b \left (\frac {d}{d x}\textit {\_Y} \left (x \right )\right )+\left (\alpha \mathrm {sn}\left (z | x \right )^{2}+\beta \right ) \textit {\_Y} \left (x \right )+\left (-12 k^{2} \mathrm {sn}\left (z | x \right )^{2}-a \right ) \left (\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )\right )+\frac {d^{4}}{d x^{4}}\textit {\_Y} \left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\}\]