ODE
\[ 4 \left (1-x^2\right ) y''(x)-8 x y'(x)-y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.160775 (sec), leaf count = 31
\[\left \{\left \{y(x)\to \frac {2 c_1 K\left (\frac {1-x}{2}\right )}{\pi }+c_2 Q_{-\frac {1}{2}}(x)\right \}\right \}\]
Maple ✓
cpu = 0.232 (sec), leaf count = 15
\[\left [y \left (x \right ) = \textit {\_C1} \LegendreP \left (-\frac {1}{2}, x\right )+\textit {\_C2} \LegendreQ \left (-\frac {1}{2}, x\right )\right ]\] Mathematica raw input
DSolve[-y[x] - 8*x*y'[x] + 4*(1 - x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (2*C[1]*EllipticK[(1 - x)/2])/Pi + C[2]*LegendreQ[-1/2, x]}}
Maple raw input
dsolve(4*(-x^2+1)*diff(diff(y(x),x),x)-8*x*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*LegendreP(-1/2,x)+_C2*LegendreQ(-1/2,x)]