\[ -y''(x) \left (a+12 k^2 \text {sn}(z|x)^2\right )+y(x) \left (\alpha \text {sn}(z|x)^2+\beta \right )+b y'(x)+y^{(4)}(x)=0 \] ✗ Mathematica : cpu = 0.0627974 (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
\[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac {{\rm d}^{4}}{{\rm d}{x}^{4}}}{\it \_Y} \left ( x \right ) + \left ( -12\,{k}^{2} \left ( {\it JacobiSN} \left ( z,x \right ) \right ) ^{2}-a \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) +b{\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) + \left ( \alpha \, \left ( {\it JacobiSN} \left ( z,x \right ) \right ) ^{2}+\beta \right ) {\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]