ODE
\[ 4 x^2 y''(x)-\left (-4 x^2+4 x+1\right ) y(x)+4 (1-2 x) x y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0190865 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \frac {e^x \left (c_2 x+c_1\right )}{\sqrt {x}}\right \}\right \}\]
Maple ✓
cpu = 0.05 (sec), leaf count = 15
\[ \left \{ y \left ( x \right ) ={{{\rm e}^{x}} \left ( x{\it \_C2}+{\it \_C1} \right ) {\frac {1}{\sqrt {x}}}} \right \} \] Mathematica raw input
DSolve[-((1 + 4*x - 4*x^2)*y[x]) + 4*(1 - 2*x)*x*y'[x] + 4*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (E^x*(C[1] + x*C[2]))/Sqrt[x]}}
Maple raw input
dsolve(4*x^2*diff(diff(y(x),x),x)+4*x*(1-2*x)*diff(y(x),x)-(-4*x^2+4*x+1)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = exp(x)*(_C2*x+_C1)/x^(1/2)