4.33.22 \(4 x^2 y''(x)+y(x)=0\)

ODE
\[ 4 x^2 y''(x)+y(x)=0 \] ODE Classification

[[_Emden, _Fowler]]

Book solution method
TO DO

Mathematica
cpu = 0.163861 (sec), leaf count = 24

\[\left \{\left \{y(x)\to \frac {1}{2} \sqrt {x} (c_2 \log (x)+2 c_1)\right \}\right \}\]

Maple
cpu = 0.011 (sec), leaf count = 17

\[\left [y \left (x \right ) = \textit {\_C1} \sqrt {x}+\textit {\_C2} \sqrt {x}\, \ln \left (x \right )\right ]\] Mathematica raw input

DSolve[y[x] + 4*x^2*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (Sqrt[x]*(2*C[1] + C[2]*Log[x]))/2}}

Maple raw input

dsolve(4*x^2*diff(diff(y(x),x),x)+y(x) = 0, y(x))

Maple raw output

[y(x) = _C1*x^(1/2)+_C2*x^(1/2)*ln(x)]