2.1267   ODE No. 1267

\[ -\left (l+2 x^2-5 x\right ) y'(x)+2 x^2 y''(x)+(1-4 x) y(x)=0 \] Mathematica : cpu = 0.35718 (sec), leaf count = 166


\[\left \{\left \{y(x)\to \frac {c_1 e^{x-\frac {l}{2 x}}}{\sqrt {x}}-\frac {\sqrt {\frac {\pi }{2}} c_2 e^{-\frac {l}{2 x}-\sqrt {2} \sqrt {-l}+x} \left (\text {erf}\left (\frac {\sqrt {-l}}{\sqrt {2} \sqrt {x}}-\sqrt {x}\right )+e^{2 \sqrt {2} \sqrt {-l}} \text {erf}\left (\frac {\sqrt {-l}}{\sqrt {2} \sqrt {x}}+\sqrt {x}\right )-e^{2 \sqrt {2} \sqrt {-l}}+1\right )}{\sqrt {-l} \sqrt {x}}\right \}\right \}\] Maple : cpu = 0.113 (sec), leaf count = 41


\[y \relax (x ) = \frac {\left (c_{1} \left (\int \frac {{\mathrm e}^{-x} {\mathrm e}^{\frac {l}{2 x}}}{2 x^{\frac {3}{2}}}d x \right )+c_{2}\right ) {\mathrm e}^{x} {\mathrm e}^{-\frac {l}{2 x}}}{\sqrt {x}}\]