ODE
\[ 2 (1-x) x^2 y''(x)+(3-5 x) x y'(x)-(x+1) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.18051 (sec), leaf count = 31
\[\left \{\left \{y(x)\to \frac {-2 c_2 \sqrt {x}+2 c_2 \tanh ^{-1}\left (\sqrt {x}\right )+c_1}{x}\right \}\right \}\]
Maple ✓
cpu = 0.136 (sec), leaf count = 35
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{x}+\frac {\textit {\_C2} \left (2 \sqrt {x}+\ln \left (\sqrt {x}-1\right )-\ln \left (\sqrt {x}+1\right )\right )}{x}\right ]\] Mathematica raw input
DSolve[-((1 + x)*y[x]) + (3 - 5*x)*x*y'[x] + 2*(1 - x)*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1] - 2*Sqrt[x]*C[2] + 2*ArcTanh[Sqrt[x]]*C[2])/x}}
Maple raw input
dsolve(2*x^2*(1-x)*diff(diff(y(x),x),x)+x*(3-5*x)*diff(y(x),x)-(x+1)*y(x) = 0, y(x))
Maple raw output
[y(x) = 1/x*_C1+_C2/x*(2*x^(1/2)+ln(x^(1/2)-1)-ln(x^(1/2)+1))]