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)]