ODE
\[ (x+1)^3 y'''(x)+(x+1)^2 y''(x)+3 (x+1) y'(x)-8 y(x)=0 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.16035 (sec), leaf count = 34
\[\left \{\left \{y(x)\to c_3 (x+1)^2+c_1 \cos (2 \log (x+1))+c_2 \sin (2 \log (x+1))\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 30
\[[y \left (x \right ) = \left (x +1\right )^{2} \textit {\_C1} +\textit {\_C2} \sin \left (2 \ln \left (x +1\right )\right )+\textit {\_C3} \cos \left (2 \ln \left (x +1\right )\right )]\] Mathematica raw input
DSolve[-8*y[x] + 3*(1 + x)*y'[x] + (1 + x)^2*y''[x] + (1 + x)^3*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (1 + x)^2*C[3] + C[1]*Cos[2*Log[1 + x]] + C[2]*Sin[2*Log[1 + x]]}}
Maple raw input
dsolve((x+1)^3*diff(diff(diff(y(x),x),x),x)+(x+1)^2*diff(diff(y(x),x),x)+3*(x+1)*diff(y(x),x)-8*y(x) = 0, y(x))
Maple raw output
[y(x) = (x+1)^2*_C1+_C2*sin(2*ln(x+1))+_C3*cos(2*ln(x+1))]