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

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

[[_high_order, _missing_y]]

Book solution method
TO DO

Mathematica
cpu = 0.162934 (sec), leaf count = 29

\[\{\{y(x)\to (c_4-c_2) x+(c_2 x-c_1) \log (x)+c_3\}\}\]

Maple
cpu = 0.013 (sec), leaf count = 18

\[[y \left (x \right ) = \textit {\_C1} +\textit {\_C2} \ln \left (x \right )+\textit {\_C3} x +\textit {\_C4} x \ln \left (x \right )]\] Mathematica raw input

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

Mathematica raw output

{{y[x] -> C[3] + x*(-C[2] + C[4]) + (-C[1] + x*C[2])*Log[x]}}

Maple raw input

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

Maple raw output

[y(x) = _C1+_C2*ln(x)+_C3*x+_C4*x*ln(x)]