ODE
\[ -x (a x+5) y'(x)+(3 a x+5) y(x)+x^2 y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.303065 (sec), leaf count = 44
\[\left \{\left \{y(x)\to \frac {x \left (a^2 c_1 e^{a x} (a x-3)-c_2 \left (a^2 x^2+4 a x+6\right )\right )}{a^3}\right \}\right \}\]
Maple ✓
cpu = 0.106 (sec), leaf count = 33
\[[y \left (x \right ) = \textit {\_C1} x \left (a^{2} x^{2}+4 a x +6\right )+\textit {\_C2} x \,{\mathrm e}^{a x} \left (a x -3\right )]\] Mathematica raw input
DSolve[(5 + 3*a*x)*y[x] - x*(5 + a*x)*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x*(a^2*E^(a*x)*(-3 + a*x)*C[1] - (6 + 4*a*x + a^2*x^2)*C[2]))/a^3}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-x*(a*x+5)*diff(y(x),x)+(3*a*x+5)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x*(a^2*x^2+4*a*x+6)+_C2*x*exp(a*x)*(a*x-3)]