ODE
\[ 4 x^2 y''(x)+y(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0115137 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {1}{2} \sqrt {x} \left (c_2 \log (x)+2 c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 14
\[ \left \{ y \left ( x \right ) =\sqrt {x} \left ( \ln \left ( x \right ) {\it \_C2}+{\it \_C1} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = x^(1/2)*(ln(x)*_C2+_C1)