2.1224   ODE No. 1224

\[ a y(x)+\left (x^2+1\right ) y''(x)+x y'(x)=0 \] Mathematica : cpu = 0.0129596 (sec), leaf count = 30


\[\left \{\left \{y(x)\to c_1 \cos \left (\sqrt {a} \sinh ^{-1}(x)\right )+c_2 \sin \left (\sqrt {a} \sinh ^{-1}(x)\right )\right \}\right \}\] Maple : cpu = 0.014 (sec), leaf count = 23


\[y \relax (x ) = c_{1} \sin \left (\sqrt {a}\, \arcsinh \relax (x )\right )+c_{2} \cos \left (\sqrt {a}\, \arcsinh \relax (x )\right )\]