4.292   ODE No. 1292

\[ \boxed { 50\,x \left ( x-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +25\, \left ( 2\,x-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\,y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.041505 (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 = 0.047 (sec), leaf count = 31 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( \sqrt {x}+\sqrt {x-1} \right ) ^{{\frac {2}{5}}}+{{\it \_C2} \left ( \sqrt {x}+\sqrt {x-1} \right ) ^{-{\frac {2}{5}}}} \right \} \]