4.33.41 \(y(x) (a+b x)+4 (1-x) x y''(x)+2 (1-2 x) y'(x)=0\)

ODE
\[ y(x) (a+b x)+4 (1-x) x y''(x)+2 (1-2 x) y'(x)=0 \] ODE Classification

[_Jacobi]

Book solution method
TO DO

Mathematica ✗
cpu = 1.26508 (sec), leaf count = 0 , DifferentialRoot result

\[\left \{\left \{y(x)\to (x)\right \}\right \}\]

Maple ✓
cpu = 1.085 (sec), leaf count = 35

\[\left [y \left (x \right ) = \textit {\_C1} \MathieuC \left (\frac {b}{2}+a , -\frac {b}{4}, \arccos \left (\sqrt {x}\right )\right )+\textit {\_C2} \MathieuS \left (\frac {b}{2}+a , -\frac {b}{4}, \arccos \left (\sqrt {x}\right )\right )\right ]\] Mathematica raw input

DSolve[(a + b*x)*y[x] + 2*(1 - 2*x)*y'[x] + 4*(1 - x)*x*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> DifferentialRoot[Function[{\[FormalY], \[FormalX]}, {(-a - \[FormalX]*
b)*\[FormalY][\[FormalX]] + (-2 + 4*\[FormalX])*Derivative[1][\[FormalY]][\[Form
alX]] + 4*(-1 + \[FormalX])*\[FormalX]*Derivative[2][\[FormalY]][\[FormalX]] == 
0, \[FormalY][2] == C[1], Derivative[1][\[FormalY]][2] == C[2]}]][x]}}

Maple raw input

dsolve(4*x*(1-x)*diff(diff(y(x),x),x)+2*(1-2*x)*diff(y(x),x)+(b*x+a)*y(x) = 0, y(x))

Maple raw output

[y(x) = _C1*MathieuC(1/2*b+a,-1/4*b,arccos(x^(1/2)))+_C2*MathieuS(1/2*b+a,-1/4*b
,arccos(x^(1/2)))]