\[ a y(x)+\left (x^2+1\right ) y''(x)+x y'(x)=0 \] ✓ Mathematica : cpu = 0.0145161 (sec), leaf count = 55
DSolve[a*y[x] + x*Derivative[1][y][x] + (1 + x^2)*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \cos \left (\sqrt {a} \log \left (\sqrt {x^2+1}-x\right )\right )-c_2 \sin \left (\sqrt {a} \log \left (\sqrt {x^2+1}-x\right )\right )\right \}\right \}\] ✓ Maple : cpu = 0.022 (sec), leaf count = 23
dsolve((x^2+1)*diff(diff(y(x),x),x)+x*diff(y(x),x)+a*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} \sin \left (\sqrt {a}\, \operatorname {arcsinh}\left (x \right )\right )+c_{2} \cos \left (\sqrt {a}\, \operatorname {arcsinh}\left (x \right )\right )\]