5.23   ODE No. 1471

\[ \boxed { {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) +f \left ( x \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +f \left ( x \right ) y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.080010 (sec), leaf count = 27 \[ \text {DSolve}\left [f(x) y''(x)+f(x) y(x)+y^{(3)}(x)+y'(x)=0,y(x),x\right ] \]

Maple: cpu = 0.156 (sec), leaf count = 36 \[ \left \{ y \left ( x \right ) ={{\rm e}^{ix}} \left ( \int \!{{\rm e}^{-2 \,ix}} \left ( \int \!{\it \_C3}\,{{\rm e}^{\int \!-f \left ( x \right ) +i\,{\rm d}x}}\,{\rm d}x+{\it \_C2} \right ) \,{\rm d}x+{\it \_C1} \right ) \right \} \]