ODE
\[ (1-x) x y''(x)+(1-x) y'(x)+2 y(x)=0 \] ODE Classification
[_Jacobi]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0811213 (sec), leaf count = 53
\[\left \{\left \{y(x)\to c_2 G_{2,2}^{2,0}\left (x\left |\begin {array}{c} 1-\sqrt {2},1+\sqrt {2} \\ 0,0 \\\end {array}\right .\right )+c_1 \, _2F_1\left (-\sqrt {2},\sqrt {2};1;x\right )\right \}\right \}\]
Maple ✓
cpu = 0.111 (sec), leaf count = 79
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\mbox {$_2$F$_1$}(-\sqrt {2},-\sqrt {2}+1;\,1-2\,\sqrt {2};\,- \left ( -1+x \right ) ^{-1})} \left ( -1+x \right ) ^{\sqrt {2}}+{\it \_C2}\,{\mbox {$_2$F$_1$}(\sqrt {2},1+\sqrt {2};\,1+2\,\sqrt {2};\,- \left ( -1+x \right ) ^{-1})} \left ( -1+x \right ) ^{-\sqrt {2}} \right \} \] Mathematica raw input
DSolve[2*y[x] + (1 - x)*y'[x] + (1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*Hypergeometric2F1[-Sqrt[2], Sqrt[2], 1, x] + C[2]*MeijerG[{{}, {1 - Sqrt[2], 1 + Sqrt[2]}}, {{0, 0}, {}}, x]}}
Maple raw input
dsolve(x*(1-x)*diff(diff(y(x),x),x)+(1-x)*diff(y(x),x)+2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*hypergeom([-2^(1/2), -2^(1/2)+1],[1-2*2^(1/2)],-1/(-1+x))*(-1+x)^(2^(1/2))+_C2*hypergeom([2^(1/2), 1+2^(1/2)],[1+2*2^(1/2)],-1/(-1+x))*(-1+x)^(-2^(1/2))