\[ \frac {k^2 \text {cn}(x|k) \text {sn}(x|k) y'(x)}{\text {dn}(x|k)}+n^2 y(x) \text {dn}(x|k)^2+y''(x)=0 \] ✗ Mathematica : cpu = 4.03005 (sec), leaf count = 0
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]
, 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 = 0.034 (sec), leaf count = 21
dsolve(diff(diff(y(x),x),x)+k^2*JacobiSN(x,k)*JacobiCN(x,k)/JacobiDN(x,k)*diff(y(x),x)+n^2*y(x)*JacobiDN(x,k)^2=0,y(x))
\[y \left (x \right ) = c_{1} \sin \left (n \,\mathrm {am}\left (x | k \right )\right )+c_{2} \cos \left (n \,\mathrm {am}\left (x | k \right )\right )\]