2.1268   ODE No. 1268

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ y(x) (a x+b)+(2 x-1) y'(x)+2 (x-1) x y''(x)=0 \] Mathematica : cpu = 0.10551 (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 = 1.058 (sec), leaf count = 39

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it MathieuC} \left ( -a-2\,b,{\frac {a}{2}},\arccos \left ( \sqrt {x} \right ) \right ) +{\it \_C2}\,{\it MathieuS} \left ( -a-2\,b,{\frac {a}{2}},\arccos \left ( \sqrt {x} \right ) \right ) \right \} \]