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 = 0.0115137 (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)