4.141   ODE No. 1141

\[ \boxed { ax{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( bx+3\,a \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +3\,by \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.107514 (sec), leaf count = 70 \[ \left \{\left \{y(x)\to \frac {c_2 e^{-\frac {b x}{a}} \left (b^2 x^2 \text {Ei}\left (\frac {b x}{a}\right )-a e^{\frac {b x}{a}} (a+b x)\right )}{2 a^2 x^2}+c_1 e^{-\frac {b x}{a}}\right \}\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 49 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac {bx}{a}}}}+ {\it \_C2}\, \left ( {\frac {a \left ( bx+a \right ) }{{x}^{2}}}+{{\rm e} ^{-{\frac {bx}{a}}}}{\it Ei} \left ( 1,-{\frac {bx}{a}} \right ) {b}^{2} \right ) \right \} \]