ODE
\[ y(x) (a+b x)+16 x y''(x)+8 y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.174784 (sec), leaf count = 96
\[\left \{\left \{y(x)\to \sqrt {x} e^{-\frac {1}{4} i \sqrt {b} x} \left (c_1 U\left (\frac {i a}{8 \sqrt {b}}+\frac {3}{4},\frac {3}{2},\frac {1}{2} i \sqrt {b} x\right )+c_2 L_{-\frac {i a}{8 \sqrt {b}}-\frac {3}{4}}^{\frac {1}{2}}\left (\frac {1}{2} i \sqrt {b} x\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.616 (sec), leaf count = 79
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{-\frac {i \sqrt {b}\, x}{4}} \KummerM \left (\frac {i a +6 \sqrt {b}}{8 \sqrt {b}}, \frac {3}{2}, \frac {i \sqrt {b}\, x}{2}\right ) \sqrt {x}+\textit {\_C2} \,{\mathrm e}^{-\frac {i \sqrt {b}\, x}{4}} \KummerU \left (\frac {i a +6 \sqrt {b}}{8 \sqrt {b}}, \frac {3}{2}, \frac {i \sqrt {b}\, x}{2}\right ) \sqrt {x}\right ]\] Mathematica raw input
DSolve[(a + b*x)*y[x] + 8*y'[x] + 16*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (Sqrt[x]*(C[1]*HypergeometricU[3/4 + ((I/8)*a)/Sqrt[b], 3/2, (I/2)*Sqrt[b]*x] + C[2]*LaguerreL[-3/4 - ((I/8)*a)/Sqrt[b], 1/2, (I/2)*Sqrt[b]*x]))/E^((I/4)*Sqrt[b]*x)}}
Maple raw input
dsolve(16*x*diff(diff(y(x),x),x)+8*diff(y(x),x)+(b*x+a)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(-1/4*I*b^(1/2)*x)*KummerM(1/8*(I*a+6*b^(1/2))/b^(1/2),3/2,1/2*I*b^(1/2)*x)*x^(1/2)+_C2*exp(-1/4*I*b^(1/2)*x)*KummerU(1/8*(I*a+6*b^(1/2))/b^(1/2),3/2,1/2*I*b^(1/2)*x)*x^(1/2)]