ODE
\[ 4 x^2 y''(x)-8 x y'(x)+5 y(x)=0 \] ODE Classification
[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.166119 (sec), leaf count = 20
\[\left \{\left \{y(x)\to \sqrt {x} \left (c_2 x^2+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 15
\[\left [y \left (x \right ) = \textit {\_C1} \,x^{\frac {5}{2}}+\sqrt {x}\, \textit {\_C2}\right ]\] Mathematica raw input
DSolve[5*y[x] - 8*x*y'[x] + 4*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> Sqrt[x]*(C[1] + x^2*C[2])}}
Maple raw input
dsolve(4*x^2*diff(diff(y(x),x),x)-8*x*diff(y(x),x)+5*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x^(5/2)+x^(1/2)*_C2]