2.1292   ODE No. 1292

\[ 50 (x-1) x y''(x)+25 (2 x-1) y'(x)-2 y(x)=0 \]

✓ Mathematica : cpu = 0.0467636 (sec), leaf count = 61

DSolve[-2*y[x] + 25*(-1 + 2*x)*Derivative[1][y][x] + 50*(-1 + x)*x*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 \cosh \left (\frac {4}{5} \tanh ^{-1}\left (\frac {\sqrt {x-1}}{\sqrt {x}+1}\right )\right )+i c_2 \sinh \left (\frac {4}{5} \tanh ^{-1}\left (\frac {\sqrt {x-1}}{\sqrt {x}+1}\right )\right )\right \}\right \}\]

✓ Maple : cpu = 0.083 (sec), leaf count = 31

dsolve(50*x*(x-1)*diff(diff(y(x),x),x)+25*(2*x-1)*diff(y(x),x)-2*y(x)=0,y(x))
 

\[y \left (x \right ) = \frac {c_{1} \left (\sqrt {x}+\sqrt {x -1}\right )^{{4}/{5}}+c_{2}}{\left (\sqrt {x}+\sqrt {x -1}\right )^{{2}/{5}}}\]