ODE
\[ x^3 \left (a+3 x^2\right ) y'(x)+x^6 y''(x)+y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0141491 (sec), leaf count = 52
\[\left \{\left \{y(x)\to e^{\frac {a-\sqrt {a^2-4}}{4 x^2}} \left (c_1 e^{\frac {\sqrt {a^2-4}}{2 x^2}}+c_2\right )\right \}\right \}\]
Maple ✓
cpu = 0.063 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac {1}{4\,{x}^{2}} \left ( -a+\sqrt {{a}^{2}-4} \right ) }}}+{\it \_C2}\,{{\rm e}^{{\frac {1}{4\,{x}^{2}} \left ( a+\sqrt {{a}^{2}-4} \right ) }}} \right \} \] Mathematica raw input
DSolve[y[x] + x^3*(a + 3*x^2)*y'[x] + x^6*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^((a - Sqrt[-4 + a^2])/(4*x^2))*(E^(Sqrt[-4 + a^2]/(2*x^2))*C[1] + C[2])}}
Maple raw input
dsolve(x^6*diff(diff(y(x),x),x)+x^3*(3*x^2+a)*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*exp(-1/4/x^2*(-a+(a^2-4)^(1/2)))+_C2*exp(1/4/x^2*(a+(a^2-4)^(1/2)))