\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +{\frac {{k}^{2}{\it JacobiSN} \left ( x,k \right ) {\it JacobiCN} \left ( x,k \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{{\it JacobiDN} \left ( x,k \right ) }}+{n}^{2}y \left ( x \right ) \left ( {\it JacobiDN} \left ( x,k \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 26.455859 (sec), leaf count = 41 \[ \text {DSolve}\left [\frac {k^2 \text {cn}(x|k) \text {sn}(x|k) y'(x)}{\text {dn}(x|k)}+n^2 y(x) \text {dn}(x|k)^2+y''(x)=0,y(x),x\right ] \]
Maple: cpu = 0.016 (sec), leaf count = 21 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sin \left ( n{\it JacobiAM} \left ( x,k \right ) \right ) +{\it \_C2}\,\cos \left ( n{\it JacobiAM} \left ( x,k \right ) \right ) \right \} \]