1. Write and then solve for y = f(x) the differential equation for the statement: "The rate of change of y with respect to x is inversely proportional to y4." (10 points)2. Solve the differential equation dy ycos(x) dx 1+yz with the initial condition y(0) = 1. (10 points)3. a. Solve the differential equation y' = 6x,/1-y2 b. Explain why the initial value problem y'=6x /1-y2 with y(0) = 2 does not have a solution. (10 points)4. 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. (10 points) X 1 1.1 1.2 1.5 1.7 1.9 2.0 f(x) 1 3 4 6 7 8 102 5. Using 4 equal-width intervals, show that the trapezoidal rule la the average of the upper and lower sum estimates for szdx . (10 points]