2.1092   ODE No. 1092

\[ (a+x) y(x)+x y''(x)=0 \]

✓ Mathematica : cpu = 0.0543041 (sec), leaf count = 72

DSolve[(a + x)*y[x] + x*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_2 e^{-i x} x \, _1F_1\left (1-\frac {1}{4} i (-2 (a-2)-4);2;2 i x\right )+c_1 e^{-i x} x U\left (1-\frac {1}{4} i (-2 (a-2)-4),2,2 i x\right )\right \}\right \}\]

✓ Maple : cpu = 0.072 (sec), leaf count = 29

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

\[y \left (x \right ) = c_{1} \operatorname {WhittakerM}\left (-\frac {i a}{2}, \frac {1}{2}, 2 i x \right )+c_{2} \operatorname {WhittakerW}\left (-\frac {i a}{2}, \frac {1}{2}, 2 i x \right )\]