3
$\begingroup$

What are the solutions to the diff eqn: $A\dot{x} + \cos(x) - 1 = B$ subject to boundary conditions $\lim\limits_{x \to -\infty} x(t) = 0$ and $\lim\limits_{x \to +\infty} x(t) = C$, where $ A, B, C$ are constants?

  • 1
    Try writing $\dot{x} = dx/dt$, separate them to two sides, like $\displaystyle A\frac{dx}{1-\cos(x)} = B\,dt$, and integrate on both sides.2011-08-11
  • 1
    @MathChief Shouldn't it be $\displaystyle A\frac{dx}{B+1-\cos(x)} = dt$2011-08-11
  • 1
    Are these limits when $t$ (and not $x$) goes to $\pm\infty$? And are the signs of $A$, $B$ and $C$ known?2011-08-11
  • 0
    @Michael, that's right, my bad.2011-08-11

1 Answers 1