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 = 0.0616696 (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 = 0.078 (sec), leaf count = 54
\[ \left \{ y \left ( x \right ) = \left ( -1+x \right ) \left ( {\it \_C2}\,\sqrt {x}{\mbox {$_2$F$_1$}({\frac {5}{4}}+{\frac {\sqrt {5}}{4}},{\frac {5}{4}}-{\frac {\sqrt {5}}{4}};\,{\frac {3}{2}};\,x)}+{\it \_C1}\,{\mbox {$_2$F$_1$}({\frac {3}{4}}+{\frac {\sqrt {5}}{4}},{\frac {3}{4}}-{\frac {\sqrt {5}}{4}};\,{\frac {1}{2}};\,x)} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = (-1+x)*(_C2*x^(1/2)*hypergeom([5/4+1/4*5^(1/2), 5/4-1/4*5^(1/2)],[3/2],x)+_C1*hypergeom([3/4+1/4*5^(1/2), 3/4-1/4*5^(1/2)],[1/2],x))