(B)
It’s easy to see that the answer must be choice (A), (B), or (C), because
the slope field depends only on x: all the slope segments for a given x are
parallel. Also, the solution curves in the slope field are all concave up, as
they are only for choices (A) and (B). Finally, the solution curves all have
a minimum at x = 2, which is true only for differential equation (B).
(E) The solution curve is y = tan x, which we can obtain from the
differential equation y′ = 1 + y^2 with the condition y(0) = 0 as follows:
