ODE No. 1139

\[ (-a-x) y(x)+16 x y''(x)+8 y'(x)=0 \] Mathematica : cpu = 0.0098161 (sec), leaf count = 74

DSolve[(-a - x)*y[x] + 8*Derivative[1][y][x] + 16*x*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 e^{\frac {1}{4} (2 \log (x)-x)} U\left (\frac {a+6}{8},\frac {3}{2},\frac {x}{2}\right )+c_2 e^{\frac {1}{4} (2 \log (x)-x)} L_{\frac {1}{8} (-a-6)}^{\frac {1}{2}}\left (\frac {x}{2}\right )\right \}\right \}\] Maple : cpu = 0.08 (sec), leaf count = 37

dsolve(16*x*diff(diff(y(x),x),x)+8*diff(y(x),x)-(x+a)*y(x)=0,y(x))
 

\[y \left (x \right ) = \sqrt {x}\, {\mathrm e}^{-\frac {x}{4}} \left (\KummerU \left (\frac {a}{8}+\frac {3}{4}, \frac {3}{2}, \frac {x}{2}\right ) c_{2}+\KummerM \left (\frac {a}{8}+\frac {3}{4}, \frac {3}{2}, \frac {x}{2}\right ) c_{1}\right )\]