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 = 0.0659271 (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 = 0.229 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) =x \left ( \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C3}\,x+{\it \_C2}\,x\ln \left ( x \right ) +{\it \_C3}\,{x}^{2}+{\it \_C1}\,x+{\it \_C3} \right ) \right \} \] 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*(1+x)*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),'implicit')
Maple raw output
y(x) = x*(ln(x)^2*_C3*x+_C2*x*ln(x)+_C3*x^2+_C1*x+_C3)