Obtain the differential equations associated with the following general sets of curves. If there are n constants you will need an nth order differential equation. You will first need to find the general equation of the set of curves. Some of these need quite a lot of manipulation. (a) The set of circles centred at the point (-2,3). More generally, given a fixed point (a, b), what is the equation of the first order ODE representing the set of circles centred at that point?

1. Candace tried to find the derivative of the function y = h(x)e-4f(x) but her group members disagreed with her result. What did she get right? What did she get wrong? Correct her y' = h'(x)e-4f(x) + h(x)e-4f(x) (-4) work. After figuring out her error, Candace attempted to check her solution by rearranging the right side of the equation y = h(x)e-4f(x) into a fraction and using the quotient rule to differentiate. Verify the correct solution using this method.

In the problem the dot over x means the derivative, the dot over the y means the derivative, and the dot over the z means the derivative. In the first example that was sent to me, the derivatives were not included.

Please give me the solution with an explanation. Thank you!