\[ \frac {k^2 \text {cn}(x|k) \text {sn}(x|k) y'(x)}{\text {dn}(x|k)}+n^2 y(x) \text {dn}(x|k)^2+y''(x)=0 \] ✗ Mathematica : cpu = 56.4014 (sec), leaf count = 0 , could not solve
DSolve[n^2*JacobiDN[x, k]^2*y[x] + (k^2*JacobiCN[x, k]*JacobiSN[x, k]*Derivative[1][y][x])/JacobiDN[x, k] + Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 0.088 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sin \left ( n{\it JacobiAM} \left ( x,k \right ) \right ) +{\it \_C2}\,\cos \left ( n{\it JacobiAM} \left ( x,k \right ) \right ) \right \} \]