1. a. Determine whether a solution is guaranteed of the initial value problem y' = sqrt(12 - y^2), y(1) = 3. State a theorem if needed
b. The initial value problem y' = sqrt(y^2 - 25) has a unique solution guaranteed if y0 = ....
2. A disease is introduced into a community of 5000 individuals. If the rate at which the disease spreads through the community is jointly proportional to the number of people who have the disease and the number of individuals who have not caught it, write down the differential equation for the number of people, x(t) who have caught the disease by time t
b. The initial value problem y' = sqrt(y^2 - 25) has a unique solution guaranteed if y0 = ....
2. A disease is introduced into a community of 5000 individuals. If the rate at which the disease spreads through the community is jointly proportional to the number of people who have the disease and the number of individuals who have not caught it, write down the differential equation for the number of people, x(t) who have caught the disease by time t