2.1094   ODE No. 1094

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

✓ Mathematica : cpu = 0.0138091 (sec), leaf count = 41

DSolve[a*y[x] + Derivative[1][y][x] + x*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 J_0\left (2 \sqrt {a} \sqrt {x}\right )+2 c_2 Y_0\left (2 \sqrt {a} \sqrt {x}\right )\right \}\right \}\]

✓ Maple : cpu = 0.016 (sec), leaf count = 29

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

\[y \left (x \right ) = c_{1} \operatorname {BesselJ}\left (0, 2 \sqrt {a}\, \sqrt {x}\right )+c_{2} \operatorname {BesselY}\left (0, 2 \sqrt {a}\, \sqrt {x}\right )\]