2.1097   ODE No. 1097

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

✓ Mathematica : cpu = 0.0166029 (sec), leaf count = 46

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

\[\left \{\left \{y(x)\to 2 a c_1 x J_2\left (2 \sqrt {a} \sqrt {x}\right )-2 a c_2 x Y_2\left (2 \sqrt {a} \sqrt {x}\right )\right \}\right \}\]

✓ Maple : cpu = 0.016 (sec), leaf count = 31

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

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