4.35.1 \(2 (2-x) x^2 y''(x)-(4-x) x y'(x)+(3-x) y(x)=0\)

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 = 0.0435322 (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 = 0.025 (sec), leaf count = 19

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {x}+{\it \_C2}\,\sqrt {x \left ( x-2 \right ) } \right \} \] 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),'implicit')

Maple raw output

y(x) = _C1*x^(1/2)+_C2*(x*(x-2))^(1/2)