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 = 0.0215898 (sec), leaf count = 24
\[\left \{\left \{y(x)\to -\frac {c_2}{2 x^2}-\frac {c_1}{x}+c_3\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 16
\[ \left \{ y \left ( x \right ) ={\it \_C1}+{\frac {{\it \_C2}}{x}}+{\frac {{\it \_C3}}{{x}^{2}}} \right \} \] Mathematica raw input
DSolve[6*y'[x] + 6*x*y''[x] + x^2*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(C[1]/x) - C[2]/(2*x^2) + 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),'implicit')
Maple raw output
y(x) = _C1+_C2/x+_C3/x^2