4.45.6 $$(x+1) x^3 y'''(x)-2 (2 x+1) x^2 y''(x)+2 (5 x+2) x y'(x)-4 (3 x+1) y(x)=0$$

ODE
$(x+1) x^3 y'''(x)-2 (2 x+1) x^2 y''(x)+2 (5 x+2) x y'(x)-4 (3 x+1) y(x)=0$ ODE Classiﬁcation

[[_3rd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.209502 (sec), leaf count = 29

$\left \{\left \{y(x)\to x^2 \left (c_3 \left (x+\frac {1}{x}+\log ^2(x)\right )+c_2 \log (x)+c_1\right )\right \}\right \}$

Maple
cpu = 0.369 (sec), leaf count = 31

$[y \left (x \right ) = x^{2} \textit {\_C1} +\textit {\_C2} \,x^{2} \ln \left (x \right )+\textit {\_C3} \left (\ln \left (x \right )^{2} x +x^{2}+1\right ) x]$ Mathematica raw input

DSolve[-4*(1 + 3*x)*y[x] + 2*x*(2 + 5*x)*y'[x] - 2*x^2*(1 + 2*x)*y''[x] + x^3*(1 + x)*y'''[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(x^3*(x+1)*diff(diff(diff(y(x),x),x),x)-2*x^2*(1+2*x)*diff(diff(y(x),x),x)+2*x*(2+5*x)*diff(y(x),x)-4*(1+3*x)*y(x) = 0, y(x))

Maple raw output

[y(x) = x^2*_C1+_C2*x^2*ln(x)+_C3*(ln(x)^2*x+x^2+1)*x]