4.100   ODE No. 1100

\[ \boxed { x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +2\,{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -xy \left ( x \right ) -{{\rm e}^{x}}=0} \]

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

Mathematica: cpu = 0.021503 (sec), leaf count = 44 \[ \left \{\left \{y(x)\to \frac {c_1 e^{-x}}{x}+\frac {c_2 e^x}{2 x}+\frac {e^x (2 x-1)}{4 x}\right \}\right \} \]

Maple: cpu = 0.032 (sec), leaf count = 23 \[ \left \{ y \left ( x \right ) ={\frac {\sinh \left ( x \right ) {\it \_C2} }{x}}+{\frac {\cosh \left ( x \right ) {\it \_C1}}{x}}+{\frac {{{\rm e}^ {x}}}{2}} \right \} \]