2.1103   ODE No. 1103

\[ a y(x)+x y''(x)-2 y'(x)=0 \]

✓ Mathematica : cpu = 0.0164703 (sec), leaf count = 64

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

\[\left \{\left \{y(x)\to 6 a^{3/2} c_1 x^{3/2} J_3\left (2 \sqrt {a} \sqrt {x}\right )-2 i a^{3/2} c_2 x^{3/2} Y_3\left (2 \sqrt {a} \sqrt {x}\right )\right \}\right \}\]

✓ Maple : cpu = 0.016 (sec), leaf count = 33

dsolve(x*diff(diff(y(x),x),x)-2*diff(y(x),x)+a*y(x)=0,y(x))
 

\[y \left (x \right ) = x^{{3}/{2}} \left (\operatorname {BesselY}\left (3, 2 \sqrt {a}\, \sqrt {x}\right ) c_{2} +\operatorname {BesselJ}\left (3, 2 \sqrt {a}\, \sqrt {x}\right ) c_{1} \right )\]