ODE
\[ x^2 y'''(x)+a x^2 y(x)+6 x y''(x)+6 y'(x)=0 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.389337 (sec), leaf count = 58
\[\left \{\left \{y(x)\to \frac {c_1 e^{-\sqrt [3]{a} x}+c_2 e^{\sqrt [3]{-1} \sqrt [3]{a} x}+c_3 e^{-(-1)^{2/3} \sqrt [3]{a} x}}{x^2}\right \}\right \}\]
Maple ✓
cpu = 0.067 (sec), leaf count = 67
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \,{\mathrm e}^{\left (-\frac {\left (-a \right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (-a \right )^{\frac {1}{3}}}{2}\right ) x}+\textit {\_C2} \,{\mathrm e}^{\left (-\frac {\left (-a \right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (-a \right )^{\frac {1}{3}}}{2}\right ) x}+\textit {\_C3} \,{\mathrm e}^{\left (-a \right )^{\frac {1}{3}} x}}{x^{2}}\right ]\] Mathematica raw input
DSolve[a*x^2*y[x] + 6*y'[x] + 6*x*y''[x] + x^2*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1]/E^(a^(1/3)*x) + E^((-1)^(1/3)*a^(1/3)*x)*C[2] + C[3]/E^((-1)^(2/3)*a^(1/3)*x))/x^2}}
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)+a*x^2*y(x) = 0, y(x))
Maple raw output
[y(x) = 1/x^2*(_C1*exp((-1/2*(-a)^(1/3)+1/2*I*3^(1/2)*(-a)^(1/3))*x)+_C2*exp((-1/2*(-a)^(1/3)-1/2*I*3^(1/2)*(-a)^(1/3))*x)+_C3*exp((-a)^(1/3)*x))]