Question: Question 1 (Essay Worth 10 points) (07.01) Write and then solve for the differential equation for the statement: The rate of change of y with

10 points) (07.02) a. Solve the differential equation y' = 4x /1-y2

. b. b. Explain why the initial value problem y' = 4x

Question 1 (Essay Worth 10 points) (07.01) Write and then solve for the differential equation for the statement: "The rate of change of y with respect to x is inversely proportional to y . Question 2 (Essay Worth 10 points) (07.02) Solve the differential equation 3: = W with the initial condition y(0) = 1. Question 3 (Essay Worth 10 points) (07.02) a. Solve the differential equation y' = 4x /1-y2 . b. b. Explain why the initial value problem y' = 4x 1-y2 with y(0) = 4 does not have a solution.Question 4 (Essay Worth 10 points) (07.03) The table below gives selected values for the function f(x). Use a trapezoidal estimation, with 6 trapezoids to approximate the value of f(x)dx . Give 3 decimal places for your answer. X 1.1 1.3 1.6 1.7 1.8 2.0 f(x) 3 5 10 11 14Question 5 (Essay Worth 10 points) (07.03) 4 Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for gxzdx

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