4.46.11 \(x^4 y''''(x)+6 x^3 y'''(x)+4 x^2 y''(x)-2 x y'(x)-4 y(x)=0\)

ODE
\[ x^4 y''''(x)+6 x^3 y'''(x)+4 x^2 y''(x)-2 x y'(x)-4 y(x)=0 \] ODE Classification

[[_high_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.0128049 (sec), leaf count = 30

\[\left \{\left \{y(x)\to c_4 x^2+\frac {c_3}{x^2}+c_2 \sin (\log (x))+c_1 \cos (\log (x))\right \}\right \}\]

Maple
cpu = 0.01 (sec), leaf count = 25

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{2}+{\frac {{\it \_C2}}{{x}^{2}}}+{\it \_C3}\,\sin \left ( \ln \left ( x \right ) \right ) +{\it \_C4}\,\cos \left ( \ln \left ( x \right ) \right ) \right \} \] Mathematica raw input

DSolve[-4*y[x] - 2*x*y'[x] + 4*x^2*y''[x] + 6*x^3*y'''[x] + x^4*y''''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[3]/x^2 + x^2*C[4] + C[1]*Cos[Log[x]] + C[2]*Sin[Log[x]]}}

Maple raw input

dsolve(x^4*diff(diff(diff(diff(y(x),x),x),x),x)+6*x^3*diff(diff(diff(y(x),x),x),x)+4*x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)-4*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*x^2+_C2/x^2+_C3*sin(ln(x))+_C4*cos(ln(x))