2.1074   ODE No. 1074

1. Problem in Latex
2. Mathematica input
3. Maple input

$$\frac{k^2\text{cn}(x|k)\text{sn}(x|k)y^{\prime }(x)}{\text{dn}(x|k)}+n^{2}y(x)\text{dn}(x|k{)}^2+y^{″}(x)=0$$ ✗ Mathematica : cpu = 4.9093 (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 = 0.1 (sec), leaf count = 21

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sin \left(n\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{A}\mathit{M}(x,k)\right)+\mathit{\_}\mathit{C}\mathit{2}\cos \left(n\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{A}\mathit{M}(x,k)\right)\}$$