Mathematica VectorPlot ***Hold***

Question

I need to solve and plot the slope field for the equation y'=cos(y)-1.

DSolve[{y'[x] == -1 + Cos[y[x]]}, y[x], x]

VectorPlot[{1, (-1 + Cos (y))}, {x, -3, 3}, {y, -3, 3}]

I get an empty graph. Any help?

Answer 1

As suggested in the comment, you are suppose to use Cos[] not Cos() in Mathematica.

You can solve the ode and combine the VectorPlot with the solution curves like this

soln[y0_?NumericQ] :=First@DSolve[{y'[x] == -1 + Cos[y[x]], y[0] == y0}, {y}, {x, 0,10}];
vp = VectorPlot[{1, (-1 + Cos[y])}, {x, -3, 3}, {y, -3, 3}];
Show[vp, Plot[
  Evaluate[{y[x]} /. soln[#] & /@ Range[-20, 20, 0.3]], {x, -3, 3}, 
  PlotRange -> All, MaxRecursion -> 8, AxesLabel -> {"x", "y"}]]