2.1105   ODE No. 1105

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

✓ Mathematica : cpu = 0.0121262 (sec), leaf count = 64

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

\[\left \{\left \{y(x)\to c_1 x^{\frac {1-a}{2}} J_{\frac {a-1}{2}}\left (\sqrt {b} x\right )+c_2 x^{\frac {1-a}{2}} Y_{\frac {a-1}{2}}\left (\sqrt {b} x\right )\right \}\right \}\]

✓ Maple : cpu = 0.062 (sec), leaf count = 39

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

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