ODE
\[ 2 x^2 (a+x) y'(x)+b y(x)+x^4 y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.170998 (sec), leaf count = 51
\[\left \{\left \{y(x)\to e^{\frac {a-\sqrt {a^2-b}}{x}} \left (c_1 e^{\frac {2 \sqrt {a^2-b}}{x}}+c_2\right )\right \}\right \}\]
Maple ✓
cpu = 0.145 (sec), leaf count = 43
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{\frac {a -\sqrt {a^{2}-b}}{x}}+\textit {\_C2} \,{\mathrm e}^{\frac {a +\sqrt {a^{2}-b}}{x}}\right ]\] Mathematica raw input
DSolve[b*y[x] + 2*x^2*(a + x)*y'[x] + x^4*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^((a - Sqrt[a^2 - b])/x)*(E^((2*Sqrt[a^2 - b])/x)*C[1] + C[2])}}
Maple raw input
dsolve(x^4*diff(diff(y(x),x),x)+2*x^2*(a+x)*diff(y(x),x)+b*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(1/x*(a-(a^2-b)^(1/2)))+_C2*exp(1/x*(a+(a^2-b)^(1/2)))]