The figure (which is not pictured, sorry) shows the slope field for y =.2(9-y^2). Make a sketch of the solution using the initial value y(-4)=-2. Find the function f(x) that this solution curve is approaching as x-->infinity. I need help with finding the function f(x) that the solution curve is approaching as x-->infinity. Thank you!
Assuming you mean
y = .2(9-x^2)
Clearly, y(-4) ≠ -2
So, let's work with something like
y' = .2(9-x^2)
Then there will be families of arrows following trajectories of parabolas.
You can find a nice online site at
https://www.desmos.com/calculator/p7vd3cdmei
Just type in your function and then pick the one where y(-4) = -2.