ODE
\[ 2 (2-x) x^2 y''(x)-(4-x) x y'(x)+(3-x) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.187118 (sec), leaf count = 41
\[\left \{\left \{y(x)\to \frac {\sqrt [4]{x-2} \sqrt {x} \left (2 c_2 \sqrt {x-2}+c_1\right )}{\sqrt [4]{2-x}}\right \}\right \}\]
Maple ✓
cpu = 0.073 (sec), leaf count = 19
\[\left [y \left (x \right ) = \textit {\_C1} \sqrt {x}+\textit {\_C2} \sqrt {x \left (x -2\right )}\right ]\] Mathematica raw input
DSolve[(3 - x)*y[x] - (4 - x)*x*y'[x] + 2*(2 - x)*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ((-2 + x)^(1/4)*Sqrt[x]*(C[1] + 2*Sqrt[-2 + x]*C[2]))/(2 - x)^(1/4)}}
Maple raw input
dsolve(2*x^2*(2-x)*diff(diff(y(x),x),x)-x*(4-x)*diff(y(x),x)+(3-x)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x^(1/2)+_C2*(x*(x-2))^(1/2)]