\[ y(x) \left (a \text {sn}(x|k)^2+b\right )+y''(x)=0 \] ✓ Mathematica : cpu = 0.753797 (sec), leaf count = 235
\[\left \{\left \{y(x)\to c_1 \sqrt {k \text {sn}(x|k)^2-1} \text {HeunG}\left [\frac {1}{k},-\frac {b-k}{4 k},\frac {\sqrt {k-4 a}+3 \sqrt {k}}{4 \sqrt {k}},\frac {\sqrt {k} \sqrt {k-4 a}+2 a+k}{2 \sqrt {k} \left (\sqrt {k-4 a}+\sqrt {k}\right )},\frac {1}{2},\frac {1}{2},\text {sn}(x|k)^2\right ]+c_2 \text {sn}(x|k) \sqrt {k \text {sn}(x|k)^2-1} \text {HeunG}\left [\frac {1}{k},-\frac {b-4 k-1}{4 k},\frac {\sqrt {k-4 a}+5 \sqrt {k}}{4 \sqrt {k}},\frac {\sqrt {k} \sqrt {k-4 a}+a+k}{\sqrt {k} \left (\sqrt {k-4 a}+\sqrt {k}\right )},\frac {3}{2},\frac {1}{2},\text {sn}(x|k)^2\right ]\right \}\right \}\] ✓ Maple : cpu = 3.557 (sec), leaf count = 69
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it HeunG} \left ( {k}^{-2},{\frac {b}{4\,{k}^{2}}},-{\frac {n}{2}},{\frac {n}{2}}+{\frac {1}{2}},{\frac {1}{2}},{\frac {1}{2}}, \left ( {\it JacobiSN} \left ( x,k \right ) \right ) ^{2} \right ) +{\it \_C2}\,{\it HeunG} \left ( {k}^{-2},{\frac {{k}^{2}+b+1}{4\,{k}^{2}}},{\frac {n}{2}}+1,-{\frac {n}{2}}+{\frac {1}{2}},{\frac {3}{2}},{\frac {1}{2}}, \left ( {\it JacobiSN} \left ( x,k \right ) \right ) ^{2} \right ) {\it JacobiSN} \left ( x,k \right ) \right \} \]