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]