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 = 0.0129671 (sec), leaf count = 34
\[\left \{\left \{y(x)\to c_3 (x+1)^2+c_2 \sin (2 \log (x+1))+c_1 \cos (2 \log (x+1))\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( 1+x \right ) ^{2}+{\it \_C2}\,\sin \left ( 2\,\ln \left ( 1+x \right ) \right ) +{\it \_C3}\,\cos \left ( 2\,\ln \left ( 1+x \right ) \right ) \right \} \] 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((1+x)^3*diff(diff(diff(y(x),x),x),x)+(1+x)^2*diff(diff(y(x),x),x)+3*(1+x)*diff(y(x),x)-8*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*(1+x)^2+_C2*sin(2*ln(1+x))+_C3*cos(2*ln(1+x))