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 = 0.0153446 (sec), leaf count = 96
\[\left \{\left \{y(x)\to \sqrt {x} e^{-\frac {1}{4} i \sqrt {b} x} \left (c_1 U\left (\frac {i a}{8 \sqrt {b}}+\frac {3}{4},\frac {3}{2},\frac {1}{2} i \sqrt {b} x\right )+c_2 L_{-\frac {3}{4}-\frac {i a}{8 \sqrt {b}}}^{\frac {1}{2}}\left (\frac {1}{2} i \sqrt {b} x\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.18 (sec), leaf count = 69
\[ \left \{ y \left ( x \right ) =\sqrt {x}{{\rm e}^{-{\frac {i}{4}}\sqrt {b}x}} \left ( {{\sl U}\left ({\frac {1}{8} \left ( ia+6\,\sqrt {b} \right ) {\frac {1}{\sqrt {b}}}},\,{\frac {3}{2}},\,{\frac {i}{2}}\sqrt {b}x\right )}{\it \_C2}+{{\sl M}\left ({\frac {1}{8} \left ( ia+6\,\sqrt {b} \right ) {\frac {1}{\sqrt {b}}}},\,{\frac {3}{2}},\,{\frac {i}{2}}\sqrt {b}x\right )}{\it \_C1} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = x^(1/2)*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)*_C2+KummerM(1/8*(I*a+6*b^(1/2))/b^(1/2),3/2,1/2*I*b^(1/2)*x)*_C1)