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 = 0.0618434 (sec), leaf count = 46
\[\left \{\left \{y(x)\to \frac {-2 c_2 \sqrt {x}-c_2 \log \left (1-\sqrt {x}\right )+c_2 \log \left (\sqrt {x}+1\right )+c_1}{x}\right \}\right \}\]
Maple ✓
cpu = 0.033 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{x}}+{\frac {{\it \_C2}}{x} \left ( 2\,\sqrt {x}+\ln \left ( \sqrt {x}-1 \right ) -\ln \left ( \sqrt {x}+1 \right ) \right ) } \right \} \] 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] - C[2]*Log[1 - Sqrt[x]] + C[2]*Log[1 + Sqrt[x]])/x}}
Maple raw input
dsolve(2*x^2*(1-x)*diff(diff(y(x),x),x)+x*(3-5*x)*diff(y(x),x)-(1+x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1/x+_C2/x*(2*x^(1/2)+ln(x^(1/2)-1)-ln(x^(1/2)+1))