2.1223   ODE No. 1223

\[ \left (x^2+1\right ) y''(x)+x y'(x)-9 y(x)=0 \]

✓ Mathematica : cpu = 0.0163028 (sec), leaf count = 45

DSolve[-9*y[x] + x*Derivative[1][y][x] + (1 + x^2)*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 \cosh \left (3 \tanh ^{-1}\left (\frac {x}{\sqrt {x^2+1}}\right )\right )+i c_2 \sinh \left (3 \tanh ^{-1}\left (\frac {x}{\sqrt {x^2+1}}\right )\right )\right \}\right \}\]

✓ Maple : cpu = 0.039 (sec), leaf count = 31

dsolve((x^2+1)*diff(diff(y(x),x),x)+x*diff(y(x),x)-9*y(x)=0,y(x))
 

\[y \left (x \right ) = \sqrt {x^{2}+1}\, \left (4 x^{2}+1\right ) c_{2} +4 c_{1} x^{3}+3 x c_{1}\]