2.1235   ODE No. 1235

\[ a y(x)+\left (x^2-1\right ) y''(x)+x y'(x)=0 \]

✓ Mathematica : cpu = 0.017783 (sec), leaf count = 50

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

\[\left \{\left \{y(x)\to c_1 \cos \left (\sqrt {a} \tanh ^{-1}\left (\frac {x}{\sqrt {x^2-1}}\right )\right )+c_2 \sin \left (\sqrt {a} \tanh ^{-1}\left (\frac {x}{\sqrt {x^2-1}}\right )\right )\right \}\right \}\]

✓ Maple : cpu = 0.05 (sec), leaf count = 45

dsolve((x^2-1)*diff(diff(y(x),x),x)+x*diff(y(x),x)+a*y(x)=0,y(x))
 

\[y \left (x \right ) = \left (c_{1} \left (x +\sqrt {x^{2}-1}\right )^{2 i \sqrt {a}}+c_{2} \right ) \left (x +\sqrt {x^{2}-1}\right )^{-i \sqrt {a}}\]