2.1402   ODE No. 1402

\[ y''(x)=-\frac {y(x) \left (4 a (a+1) x^4-2 a \left (x^2-1\right ) x^2+\left (x^2-1\right )^2 \left (x^2-v^2\right )\right )}{x^2 \left (x^2-1\right )^2}-\frac {\left ((1-4 a) x^2-1\right ) y'(x)}{x \left (x^2-1\right )} \] Mathematica : cpu = 0.808127 (sec), leaf count = 86


\[\left \{\left \{y(x)\to c_2 \left (x^2-1\right )^{a+1} x^{-v} \text {HeunC}\left [-\frac {a}{2}+v-\frac {3}{4},\frac {1}{4},1-v,2,0,x^2\right ]+c_1 \left (x^2-1\right )^{a+1} x^v \text {HeunC}\left [\frac {1}{4} (-2 a-4 v-3),\frac {1}{4},v+1,2,0,x^2\right ]\right \}\right \}\] Maple : cpu = 0.229 (sec), leaf count = 58


\[y \relax (x ) = \left (x^{2}-1\right )^{a} \left (x^{2}-1\right ) \left (c_{1} x^{v} \HeunC \left (0, v , 1, \frac {1}{4}, \frac {a}{2}+\frac {1}{4}, x^{2}\right )+c_{2} x^{-v} \HeunC \left (0, -v , 1, \frac {1}{4}, \frac {a}{2}+\frac {1}{4}, x^{2}\right )\right )\]