2.1204   ODE No. 1204

\[ x^2 (a+2 b) y'(x)+y(x) \left (b x^2 (a+b)-2\right )+x^2 y''(x)=0 \] Mathematica : cpu = 0.0146681 (sec), leaf count = 132


\[\left \{\left \{y(x)\to \frac {2 c_2 e^{\frac {1}{2} (-a x-2 b x+\log (x))} \left (i \sinh \left (\frac {a x}{2}\right )-\frac {2 i \cosh \left (\frac {a x}{2}\right )}{a x}\right )}{\sqrt {\pi } \sqrt {-i a x}}+\frac {2 c_1 e^{\frac {1}{2} (-a x-2 b x+\log (x))} \left (\frac {2 \sinh \left (\frac {a x}{2}\right )}{a x}-\cosh \left (\frac {a x}{2}\right )\right )}{\sqrt {\pi } \sqrt {-i a x}}\right \}\right \}\] Maple : cpu = 0.043 (sec), leaf count = 35


\[y \relax (x ) = \frac {c_{2} \left (a x +2\right ) {\mathrm e}^{-\left (a +b \right ) x}+c_{1} {\mathrm e}^{-b x} \left (a x -2\right )}{x}\]