\[ 50 (x-1) x y''(x)+25 (2 x-1) y'(x)-2 y(x)=0 \] ✓ Mathematica : cpu = 0.0323796 (sec), leaf count = 42
DSolve[-2*y[x] + 25*(-1 + 2*x)*Derivative[1][y][x] + 50*(-1 + x)*x*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_2 \sin \left (\frac {2}{5} \sin ^{-1}\left (\sqrt {1-x}\right )\right )+c_1 \cos \left (\frac {2}{5} \sin ^{-1}\left (\sqrt {1-x}\right )\right )\right \}\right \}\] ✓ Maple : cpu = 0.05 (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))
\[y \left (x \right ) = \frac {c_{1} \left (\sqrt {x}+\sqrt {x -1}\right )^{\frac {4}{5}}+c_{2}}{\left (\sqrt {x}+\sqrt {x -1}\right )^{\frac {2}{5}}}\]