2.1190   ODE No. 1190

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

\[ y(x) (a x+b)+x^2 y''(x)+x^2 y'(x)=0 \] Mathematica : cpu = 0.0311144 (sec), leaf count = 95

\[\left \{\left \{y(x)\to e^{-x} x^{\frac {1}{2} \left (\sqrt {1-4 b}+1\right )} \left (c_1 U\left (\frac {1}{2} \left (-2 a+\sqrt {1-4 b}+1\right ),\sqrt {1-4 b}+1,x\right )+c_2 L_{a-\frac {1}{2} \sqrt {1-4 b}-\frac {1}{2}}^{\sqrt {1-4 b}}(x)\right )\right \}\right \}\]

Maple : cpu = 0.09 (sec), leaf count = 38

\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {x}{2}}}} \left ( {{\sl W}_{a,\,{\frac {1}{2}\sqrt {1-4\,b}}}\left (x\right )}{\it \_C2}+{{\sl M}_{a,\,{\frac {1}{2}\sqrt {1-4\,b}}}\left (x\right )}{\it \_C1} \right ) \right \} \]