1. The problem statement, all variables and given/known data (i've put my questions in bold) The differential equation is dy/dx = xy^2 I separated variables and came up with (solving for c) c = -1/y - (x^2)/2 I then had to find the particular solution for y(0) = 1, so I came up with c = -1 - 0 so c = -1 I then solved for y and got that y = -1/(1-(x^2)/2) ... is this the correct answer for the specific solution? Finally, I had to determine what values of C gave the diff eq. vertical asymptotes. I know this happens when the denominator equals zero, so I said that it is the case when c+(x^2)/2 = 0. This only happens when C = 0 and x = 0. Correct? 1. The problem statement, all variables and given/known data The second question: the function G(x) = G(-4) + antiderivative from -4 to x of f(t) dt over the interval [-4,3] I have the graph of f, however, so when I take G'(x) I get f(x), correct? What about the G(-2)? That's the part I am not sure of. I'm assuming that it doesn't matter since the interval runs from [-4,3] and the antiderivative from -4 to -4 is simply zero. Is this the right way of looking at it? Thanks.