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 = 0.270551 (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 = 0.018 (sec), leaf count = 62
\[ \left \{ y \left ( x \right ) +{\frac {1}{{x}^{2}} \left ( -{\it \_C1}\,{{\rm e}^{{\frac { \left ( i\sqrt {3}-1 \right ) x}{2}\sqrt [3]{-a}}}}-{\it \_C2}\,{{\rm e}^{-{\frac { \left ( i\sqrt {3}+1 \right ) x}{2}\sqrt [3]{-a}}}}-{\it \_C3}\,{{\rm e}^{\sqrt [3]{-a}x}} \right ) }=0 \right \} \] 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),'implicit')
Maple raw output
y(x)+(-_C1*exp(1/2*(-a)^(1/3)*(I*3^(1/2)-1)*x)-_C2*exp(-1/2*(-a)^(1/3)*(I*3^(1/2)+1)*x)-_C3*exp((-a)^(1/3)*x))/x^2 = 0