4.32.12 \((1-x) x y''(x)-2 y'(x)+2 y(x)=0\)

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

[[_2nd_order, _exact, _linear, _homogeneous]]

Book solution method
TO DO

Mathematica
cpu = 0.0170453 (sec), leaf count = 24

\[\left \{\left \{y(x)\to \frac {c_2 x^3+3 c_1}{3-3 x}\right \}\right \}\]

Maple
cpu = 0.02 (sec), leaf count = 17

\[ \left \{ y \left ( x \right ) ={\frac {{x}^{3}{\it \_C2}+{\it \_C1}}{-1+x}} \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> (3*C[1] + x^3*C[2])/(3 - 3*x)}}

Maple raw input

dsolve(x*(1-x)*diff(diff(y(x),x),x)-2*diff(y(x),x)+2*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (_C2*x^3+_C1)/(-1+x)