ODE
\[ x (2-x)^2 y''(x)+2 (2-x) y'(x)+2 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.02554 (sec), leaf count = 32
\[\left \{\left \{y(x)\to -\frac {1}{2} (x-2) \left (-c_2 \log (2-x)+c_2 \log (x)+2 c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) = \left ( x-2 \right ) \left ( {\it \_C2}\,\ln \left ( x-2 \right ) -{\it \_C2}\,\ln \left ( x \right ) +{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[2*y[x] + 2*(2 - x)*y'[x] + (2 - x)^2*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -((-2 + x)*(2*C[1] - C[2]*Log[2 - x] + C[2]*Log[x]))/2}}
Maple raw input
dsolve(x*(2-x)^2*diff(diff(y(x),x),x)+2*(2-x)*diff(y(x),x)+2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (x-2)*(_C2*ln(x-2)-_C2*ln(x)+_C1)