\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) - \left ( n \left ( n+1 \right ) {k}^{2} \left ( {\it JacobiSN} \left ( x,k \right ) \right ) ^{2}+b \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.995126 (sec), leaf count = 23 \[ \text {DSolve}\left [y(x) \left (a \text {sn}(x|k)^2+b\right )+y''(x)=0,y(x),x\right ] \]
Maple: cpu = 0.265 (sec), leaf count = 69 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it HeunG} \left ( {k}^{-2},{ \frac {b}{4\,{k}^{2}}},-{\frac {n}{2}},{\frac {n}{2}}+{\frac {1}{2}},{ \frac {1}{2}},{\frac {1}{2}}, \left ( {\it JacobiSN} \left ( x,k \right ) \right ) ^{2} \right ) +{\it \_C2}\,{\it HeunG} \left ( {k}^{-2 },{\frac {{k}^{2}+b+1}{4\,{k}^{2}}},{\frac {n}{2}}+1,-{\frac {n}{2}}+{ \frac {1}{2}},{\frac {3}{2}},{\frac {1}{2}}, \left ( {\it JacobiSN} \left ( x,k \right ) \right ) ^{2} \right ) {\it JacobiSN} \left ( x,k \right ) \right \} \]