2.1292   ODE No. 1292

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

\[ 50 (x-1) x y''(x)+25 (2 x-1) y'(x)-2 y(x)=0 \] Mathematica : cpu = 0.0390016 (sec), leaf count = 53

\[\left \{\left \{y(x)\to c_1 \cosh \left (\frac {2}{5} \log \left (\sqrt {x-1}+\sqrt {x}\right )\right )+i c_2 \sinh \left (\frac {2}{5} \log \left (\sqrt {x-1}+\sqrt {x}\right )\right )\right \}\right \}\]

Maple : cpu = 0.097 (sec), leaf count = 31

\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( \sqrt {x}+\sqrt {x-1} \right ) ^{{\frac {2}{5}}}+{{\it \_C2} \left ( \sqrt {x}+\sqrt {x-1} \right ) ^{-{\frac {2}{5}}}} \right \} \]