2.16   ODE No. 16

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

\[ f(x) (x y(x)-1)+y'(x)+y(x)^2=0 \] Mathematica : cpu = 21.2663 (sec), leaf count = 0 , could not solve

DSolve[y[x]^2 + f[x]*(-1 + x*y[x]) + Derivative[1][y][x] == 0, y[x], x]

Maple : cpu = 0.111 (sec), leaf count = 50

\[ \left \{ y \left ( x \right ) =-{1{{\rm e}^{\int \!-{\frac {{x}^{2}f \left ( x \right ) +2}{x}}\,{\rm d}x}} \left ( {\it \_C1}-\int \!{{\rm e}^{\int \!-{\frac {{x}^{2}f \left ( x \right ) +2}{x}}\,{\rm d}x}}\,{\rm d}x \right ) ^{-1}}+{x}^{-1} \right \} \]