ODE
\[ 16 x^2 y''(x)+32 x y'(x)-(4 x+5) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0860775 (sec), leaf count = 51
\[\left \{\left \{y(x)\to \frac {e^{-\sqrt {x}} \left (c_2 \left (\sqrt {x}+1\right )-c_1 e^{2 \sqrt {x}} \left (\sqrt {x}-1\right )\right )}{x^{5/4}}\right \}\right \}\]
Maple ✓
cpu = 0.088 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={1 \left ( {\it \_C2}\, \left ( \sqrt {x}+1 \right ) {{\rm e}^{-\sqrt {x}}}+{\it \_C1}\,{{\rm e}^{\sqrt {x}}} \left ( \sqrt {x}-1 \right ) \right ) {x}^{-{\frac {5}{4}}}} \right \} \] Mathematica raw input
DSolve[-((5 + 4*x)*y[x]) + 32*x*y'[x] + 16*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-(E^(2*Sqrt[x])*(-1 + Sqrt[x])*C[1]) + (1 + Sqrt[x])*C[2])/(E^Sqrt[x]*x^(5/4))}}
Maple raw input
dsolve(16*x^2*diff(diff(y(x),x),x)+32*x*diff(y(x),x)-(5+4*x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C2*(x^(1/2)+1)*exp(-x^(1/2))+_C1*exp(x^(1/2))*(x^(1/2)-1))/x^(5/4)