\[ -y'(x) \left (a+3 k^2 \text {sn}(z|x)^2\right )+y(x) \left (b+c \text {sn}(z|x)^2-3 k^2 \text {cn}(z|x) \text {dn}(z|x) \text {sn}(z|x)\right )+y^{(3)}(x)=0 \] ✗ Mathematica : cpu = 0.0307655 (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
\[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}{\it \_Y} \left ( x \right ) + \left ( -3\,{k}^{2} \left ( {\it JacobiSN} \left ( z,x \right ) \right ) ^{2}-a \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) + \left ( b+c \left ( {\it JacobiSN} \left ( z,x \right ) \right ) ^{2}-3\,{k}^{2}{\it JacobiSN} \left ( z,x \right ) {\it JacobiCN} \left ( z,x \right ) {\it JacobiDN} \left ( z,x \right ) \right ) {\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]