ODE
\[ 4 (1-x) x y''(x)+2 (1-x) y'(x)+y(x)=0 \] ODE Classification
[_Jacobi]
Book solution method
TO DO
Mathematica ✓
cpu = 0.215218 (sec), leaf count = 78
\[\left \{\left \{y(x)\to c_1 \, _2F_1\left (\frac {1}{4} \left (-1-\sqrt {5}\right ),\frac {1}{4} \left (-1+\sqrt {5}\right );\frac {1}{2};x\right )+i c_2 \sqrt {x} \, _2F_1\left (\frac {1}{4} \left (1-\sqrt {5}\right ),\frac {1}{4} \left (1+\sqrt {5}\right );\frac {3}{2};x\right )\right \}\right \}\]
Maple ✓
cpu = 0.423 (sec), leaf count = 56
\[\left [y \left (x \right ) = \textit {\_C1} \left (x -1\right ) \hypergeom \left (\left [\frac {3}{4}+\frac {\sqrt {5}}{4}, \frac {3}{4}-\frac {\sqrt {5}}{4}\right ], \left [\frac {1}{2}\right ], x\right )+\textit {\_C2} \sqrt {x}\, \left (x -1\right ) \hypergeom \left (\left [\frac {5}{4}+\frac {\sqrt {5}}{4}, \frac {5}{4}-\frac {\sqrt {5}}{4}\right ], \left [\frac {3}{2}\right ], x\right )\right ]\] Mathematica raw input
DSolve[y[x] + 2*(1 - x)*y'[x] + 4*(1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*Hypergeometric2F1[(-1 - Sqrt[5])/4, (-1 + Sqrt[5])/4, 1/2, x] + I*Sqrt[x]*C[2]*Hypergeometric2F1[(1 - Sqrt[5])/4, (1 + Sqrt[5])/4, 3/2, x]}}
Maple raw input
dsolve(4*x*(1-x)*diff(diff(y(x),x),x)+2*(1-x)*diff(y(x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*(x-1)*hypergeom([3/4+1/4*5^(1/2), 3/4-1/4*5^(1/2)],[1/2],x)+_C2*x^(1/2)*(x-1)*hypergeom([5/4+1/4*5^(1/2), 5/4-1/4*5^(1/2)],[3/2],x)]