3.16   ODE No. 16

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{2}+ \left ( xy \left ( x \right ) -1 \right ) f \left ( x \right ) =0} \]

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

Mathematica: cpu = 21.387216 (sec), leaf count = 24 \[ \text {DSolve}\left [f(x) (x y(x)-1)+y'(x)+y(x)^2=0,y(x),x\right ] \]

Maple: cpu = 0.093 (sec), leaf count = 50 \[ \left \{ y \left ( x \right ) =-{1{{\rm e}^{\int \!-{\frac {{x}^{2}f \left ( x \right ) +2}{x}}\,{\rm d}x}} \left ( {\it \_C1}-\int \!{ {\rm e}^{\int \!-{\frac {{x}^{2}f \left ( x \right ) +2}{x}}\,{\rm d}x}} \,{\rm d}x \right ) ^{-1}}+{x}^{-1} \right \} \]

Sage: cpu = 0.068 (sec), leaf count = 0 \[ \left [\left [\left [y\left (x\right ) = 0, u f\left (x\right ) = 0\right ]\right ], \text {\texttt {riccati}}\right ] \]