2.1268   ODE No. 1268

\[ y(x) (a x+b)+2 (x-1) x y''(x)+(2 x-1) y'(x)=0 \] Mathematica : cpu = 0.098089 (sec), leaf count = 50


\[\left \{\left \{y(x)\to c_1 \text {MathieuC}\left [-a-2 b,\frac {a}{2},\cos ^{-1}\left (\sqrt {x}\right )\right ]+c_2 \text {MathieuS}\left [-a-2 b,\frac {a}{2},\cos ^{-1}\left (\sqrt {x}\right )\right ]\right \}\right \}\] Maple : cpu = 0.101 (sec), leaf count = 39


\[y \relax (x ) = c_{1} \MathieuC \left (-a -2 b , \frac {a}{2}, \arccos \left (\sqrt {x}\right )\right )+c_{2} \MathieuS \left (-a -2 b , \frac {a}{2}, \arccos \left (\sqrt {x}\right )\right )\]