2.1139   ODE No. 1139

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

\[ -(a+x) y(x)+8 y'(x)+16 x y''(x)=0 \] Mathematica : cpu = 0.0103289 (sec), leaf count = 74

\[\left \{\left \{y(x)\to c_1 e^{\frac {1}{4} (2 \log (x)-x)} U\left (\frac {a+6}{8},\frac {3}{2},\frac {x}{2}\right )+c_2 e^{\frac {1}{4} (2 \log (x)-x)} L_{\frac {1}{8} (-a-6)}^{\frac {1}{2}}\left (\frac {x}{2}\right )\right \}\right \}\] Maple : cpu = 0.37 (sec), leaf count = 37

\[ \left \{ y \left ( x \right ) =\sqrt {x}{{\rm e}^{-{\frac {x}{4}}}} \left ( {{\sl U}\left ({\frac {a}{8}}+{\frac {3}{4}},\,{\frac {3}{2}},\,{\frac {x}{2}}\right )}{\it \_C2}+{{\sl M}\left ({\frac {a}{8}}+{\frac {3}{4}},\,{\frac {3}{2}},\,{\frac {x}{2}}\right )}{\it \_C1} \right ) \right \} \]