\[ -y'(x) \left (a+3 k^2 \text {sn}(z|x)^2\right )+y(x) \left (b+c \text {sn}(z|x)^2-3 k^2 \text {cn}(z|x) \text {dn}(z|x) \text {sn}(z|x)\right )+y^{(3)}(x)=0 \] ✗ Mathematica : cpu = 0.0238438 (sec), leaf count = 0
, could not solve
DSolve[(b - 3*k^2*JacobiCN[z, x]*JacobiDN[z, x]*JacobiSN[z, x] + c*JacobiSN[z, x]^2)*y[x] - (a + 3*k^2*JacobiSN[z, x]^2)*Derivative[1][y][x] + Derivative[3][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0
, result contains DESol or ODESolStruc
\[y \relax (x ) = \mathit {DESol}\left (\left \{\frac {d^{3}}{d x^{3}}\textit {\_Y} \relax (x )+\left (-3 k^{2} \mathrm {sn}\left (z | x \right )^{2}-a \right ) \left (\frac {d}{d x}\textit {\_Y} \relax (x )\right )+\left (b +c \mathrm {sn}\left (z | x \right )^{2}-3 k^{2} \mathrm {sn}\left (z | x \right ) \mathrm {cn}\left (z | x \right ) \mathrm {dn}\left (z | x \right )\right ) \textit {\_Y} \relax (x )\right \}, \left \{\textit {\_Y} \relax (x )\right \}\right )\]