AB 5.
(b)AB 6.
(a) Using the differential equation, evaluate the derivative at each
point, then sketch a short segment having that slope. For example, at
(−1, −1), ; draw a steeply decreasing segment at
(−1,−1).
Repeat this process at each of the other points. The result follows.The differential equation is separable.It is given that f passes through (0,1), so 1 = tan (0^2 + c) and .
The solution is .
The particular solution must be differentiable on an interval containing
the initial point (0,1). The tangent function has vertical asymptotes at
, hence:. (Since x^2 ≥ 0, we ignore the left inequality.)
(a) .