This is for Calc II homework..
The figure below shows the slope field for the equation y' = sin (x) cos (y).
(If you want I can post the picture, but I don't think its needed)
And the question is
What is the equation of the solution passing through (0(2n+1)2), where n is any integer?
Now, I know that the slope is 0 along any of these points but I just don't know what to do with the rest of the information.
Thanks for any help
y' = sin (x) cos (y).
has equiilibrium solutions of the form y= constant where cos(y) = 0
which is (2n+1)pi/2
the solution curves are y = (2n+1)pi/2 which are horizontal lines
In general for dy/dx = f(x)g(y) equillibrium solutions are precisely the zeroes of g(y)