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 = 0.0391015 (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 = 0.076 (sec), leaf count = 31

\[ \left \{ y \left ( x \right ) ={1 \left ( {\it \_C1}\, \left ( \sqrt {x}+\sqrt {x-1} \right ) ^{{\frac {4}{5}}}+{\it \_C2} \right ) \left ( \sqrt {x}+\sqrt {x-1} \right ) ^{-{\frac {2}{5}}}} \right \} \]