\[ -y''(x) \left (a+12 k^2 \text {sn}(z|x)^2\right )+y(x) \left (\alpha \text {sn}(z|x)^2+\beta \right )+b y'(x)+y^{(4)}(x)=0 \] ✗ Mathematica : cpu = 0.0433851 (sec), leaf count = 0
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]
, 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
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)-(12*k^2*JacobiSN(z,x)^2+a)*diff(diff(y(x),x),x)+b*diff(y(x),x)+(alpha*JacobiSN(z,x)^2+beta)*y(x)=0,y(x))
, result contains DESol or ODESolStruc
\[y \left (x \right ) = \operatorname {DESol}\left (\left \{\frac {d^{4}}{d x^{4}}\textit {\_Y} \left (x \right )+\left (-12 k^{2} \operatorname {JacobiSN}\left (z , x\right )^{2}-a \right ) \left (\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )\right )+b \left (\frac {d}{d x}\textit {\_Y} \left (x \right )\right )+\left (\alpha \operatorname {JacobiSN}\left (z , x\right )^{2}+\beta \right ) \textit {\_Y} \left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\]