ODE
\[ x^3 y''''(x)+6 x^2 y'''(x)+6 x y''(x)=0 \] ODE Classification
[[_high_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0275706 (sec), leaf count = 27
\[\left \{\left \{y(x)\to \frac {c_2}{2 x}+c_4 x-c_1 \log (x)+c_3\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) ={\it \_C1}+{\it \_C2}\,\ln \left ( x \right ) +{\frac {{\it \_C3}}{x}}+{\it \_C4}\,x \right \} \] Mathematica raw input
DSolve[6*x*y''[x] + 6*x^2*y'''[x] + x^3*y''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[2]/(2*x) + C[3] + x*C[4] - C[1]*Log[x]}}
Maple raw input
dsolve(x^3*diff(diff(diff(diff(y(x),x),x),x),x)+6*x^2*diff(diff(diff(y(x),x),x),x)+6*x*diff(diff(y(x),x),x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1+_C2*ln(x)+_C3/x+_C4*x