4.267   ODE No. 1267

\[ \boxed { 2\,{x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) - \left ( 2\,{x}^{2}+l-5\,x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( 4\,x-1 \right ) y \left ( x \right ) =0} \]

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

Mathematica: cpu = 34.197343 (sec), leaf count = 205 \[ \left \{\left \{y(x)\to \frac {\sqrt {\frac {\pi }{2}} c_2 l \left (e^{2 \sqrt {2} \sqrt {-l}} \text {erf}\left (\frac {\sqrt {-l}}{\sqrt {2} \sqrt {x}}+\sqrt {x}\right )+\text {erf}\left (\frac {\sqrt {2} \sqrt {-l}-2 x}{2 \sqrt {x}}\right )+\text {erf}\left (1-\frac {\sqrt {-l}}{\sqrt {2}}\right )-e^{2 \sqrt {2} \sqrt {-l}} \text {erf}\left (\frac {\sqrt {-l}}{\sqrt {2}}+1\right )\right ) e^{\frac {1}{2} \left (-\frac {l}{x}+2 x-\log (x)\right )-\sqrt {2} \sqrt {-l}}}{(-l)^{3/2}}+c_1 e^{\frac {1}{2} \left (-\frac {l}{x}+2 x-\log (x)\right )}\right \}\right \} \]

Maple: cpu = 0.046 (sec), leaf count = 41 \[ \left \{ y \left ( x \right ) ={{{\rm e}^{x}} \left ( {\it \_C1}\,\int \! {\frac {1}{2\,{{\rm e}^{x}}}{{\rm e}^{{\frac {l}{2\,x}}}}{x}^{-{\frac {3}{2}}}}\,{\rm d}x+{\it \_C2} \right ) {\frac {1}{\sqrt {x}}} \left ( { {\rm e}^{{\frac {l}{2\,x}}}} \right ) ^{-1}} \right \} \]