2.1141   ODE No. 1141

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

\[ (3 a+b x) y'(x)+a x y''(x)+3 b y(x)=0 \] Mathematica : cpu = 0.119417 (sec), leaf count = 79

\[\left \{\left \{y(x)\to c_1 e^{-\frac {b x}{a}}-\frac {c_2 e^{-\frac {b x}{a}} \left (a^2 e^{\frac {b x}{a}}-b^2 x^2 \text {Ei}\left (\frac {b x}{a}\right )+a b x e^{\frac {b x}{a}}\right )}{2 a^2 x^2}\right \}\right \}\] Maple : cpu = 0.066 (sec), leaf count = 55

\[ \left \{ y \left ( x \right ) ={\frac {1}{{x}^{2}} \left ( {\it Ei} \left ( 1,-{\frac {bx}{a}} \right ) {{\rm e}^{-{\frac {bx}{a}}}}{\it \_C2}\,{b}^{2}{x}^{2}+{\it \_C1}\,{{\rm e}^{-{\frac {bx}{a}}}}{x}^{2}+a{\it \_C2}\, \left ( bx+a \right ) \right ) } \right \} \]