2.1267   ODE No. 1267

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ -\left (l+2 x^2-5 x\right ) y'(x)+2 x^2 y''(x)-(4 x-1) y(x)=0 \] Mathematica : cpu = 0.414811 (sec), leaf count = 154

\[\left \{\left \{y(x)\to \frac {e^{x-\frac {l}{2 x}} \left (\frac {\sqrt {2 \pi } c_2 e^{-\sqrt {2} \sqrt {-l}} l \left (e^{2 \sqrt {2} \sqrt {-l}} \text {erf}\left (\frac {\sqrt {-l}}{\sqrt {2} \sqrt {x}}+\sqrt {x}\right )+\text {erf}\left (\frac {\sqrt {2} \sqrt {-l}-2 x}{2 \sqrt {x}}\right )-e^{2 \sqrt {2} \sqrt {-l}}+1\right )}{(-l)^{3/2}}+2 c_1\right )}{2 \sqrt {x}}\right \}\right \}\]

Maple : cpu = 0.081 (sec), leaf count = 41

\[ \left \{ y \left ( x \right ) ={{{\rm e}^{x}} \left ( {\it \_C1}\,\int \!{\frac {1}{2\,{{\rm e}^{x}}}{{\rm e}^{{\frac {l}{2\,x}}}}{x}^{-{\frac {3}{2}}}}\,{\rm d}x+{\it \_C2} \right ) \left ( {{\rm e}^{{\frac {l}{2\,x}}}} \right ) ^{-1}{\frac {1}{\sqrt {x}}}} \right \} \]