ODE No. 1268

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

\[ y(x) (a x+b)+2 (x-1) x y''(x)+(2 x-1) y'(x)=0 \] Mathematica : cpu = 1.60679 (sec), leaf count = 0 , DifferentialRoot result

\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{(\unicode {f817} a+b) \unicode {f818}(\unicode {f817})+(2 \unicode {f817}-1) \unicode {f818}'(\unicode {f817})+2 (\unicode {f817}-1) \unicode {f817} \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(2)=c_1,\unicode {f818}'(2)=c_2\right \}\right )(x)\right \}\right \}\]

Maple : cpu = 0.146 (sec), leaf count = 39

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