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)]