ODE
\[ y(x) (a+b x)+2 (1-x) x y''(x)+(1-2 x) y'(x)=0 \] ODE Classification
[_Jacobi]
Book solution method
TO DO
Mathematica ✓
cpu = 0.256018 (sec), leaf count = 46
\[\left \{\left \{y(x)\to c_1 \text {MathieuC}\left [2 a+b,-\frac {b}{2},\cos ^{-1}\left (\sqrt {x}\right )\right ]+c_2 \text {MathieuS}\left [2 a+b,-\frac {b}{2},\cos ^{-1}\left (\sqrt {x}\right )\right ]\right \}\right \}\]
Maple ✓
cpu = 1.117 (sec), leaf count = 35
\[\left [y \left (x \right ) = \textit {\_C1} \MathieuC \left (2 a +b , -\frac {b}{2}, \arccos \left (\sqrt {x}\right )\right )+\textit {\_C2} \MathieuS \left (2 a +b , -\frac {b}{2}, \arccos \left (\sqrt {x}\right )\right )\right ]\] Mathematica raw input
DSolve[(a + b*x)*y[x] + (1 - 2*x)*y'[x] + 2*(1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*MathieuC[2*a + b, -1/2*b, ArcCos[Sqrt[x]]] + C[2]*MathieuS[2*a + b, -1/2*b, ArcCos[Sqrt[x]]]}}
Maple raw input
dsolve(2*x*(1-x)*diff(diff(y(x),x),x)+(1-2*x)*diff(y(x),x)+(b*x+a)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*MathieuC(2*a+b,-1/2*b,arccos(x^(1/2)))+_C2*MathieuS(2*a+b,-1/2*b,arccos(x^(1/2)))]