ODE
\[ x^2 y'''(x)+6 x y''(x)+6 y'(x)=0 \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.16742 (sec), leaf count = 24
\[\left \{\left \{y(x)\to -\frac {c_1}{2 x^2}-\frac {c_2}{x}+c_3\right \}\right \}\]
Maple ✓
cpu = 0.015 (sec), leaf count = 16
\[\left [y \left (x \right ) = \textit {\_C1} +\frac {\textit {\_C2}}{x^{2}}+\frac {\textit {\_C3}}{x}\right ]\] Mathematica raw input
DSolve[6*y'[x] + 6*x*y''[x] + x^2*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -1/2*C[1]/x^2 - C[2]/x + C[3]}}
Maple raw input
dsolve(x^2*diff(diff(diff(y(x),x),x),x)+6*x*diff(diff(y(x),x),x)+6*diff(y(x),x) = 0, y(x))
Maple raw output
[y(x) = _C1+_C2/x^2+1/x*_C3]