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 = 0.0252559 (sec), leaf count = 29

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

Maple
cpu = 0.009 (sec), leaf count = 17

\[ \left \{ y \left ( x \right ) = \left ( {\it \_C2}\,x+{\it \_C4} \right ) \ln \left ( x \right ) +{\it \_C1}\,x+{\it \_C3} \right \} \] 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[1] + C[4]) + (x*C[1] - 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),'implicit')

Maple raw output

y(x) = (_C2*x+_C4)*ln(x)+_C1*x+_C3