3.10   ODE No. 10

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

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

Mathematica: cpu = 0.007501 (sec), leaf count = 18 \[ \left \{\left \{y(x)\to c_1 e^{-f(x)}+f(x)-1\right \}\right \} \]

Maple: cpu = 0.015 (sec), leaf count = 15 \[ \left \{ y \left ( x \right ) =f \left ( x \right ) -1+{{\rm e}^{-f \left ( x \right ) }}{\it \_C1} \right \} \]

Sage: cpu = 0.06 (sec), leaf count = 0 \[ \left [{\left (c + \int e^{f\left (x\right )} f\left (x\right ) D[0]\left (f\right )\left (x\right )\,{d x}\right )} e^{\left (-f\left (x\right )\right )}, \text {\texttt {linear}}\right ] \]