Mathematics Homework Help

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 y^4.”

2. Solve the differential equation dy dx equals the quotient of y times the cosine of x and the quantity 1 plus y squared with the initial condition y(0) = 1.

3.

1. Solve the differential equation .
2. Explain why the initial value problem with y(0) = 2 does not have a solution.

4. The table below gives selected values for the function f(x). Use a trapezoidal estimation, with 6 trapezoids to approximate the value of the integral from 1 to 2 of f of x, dx. Give 3 decimal places for your answer.

x 1 1.1 1.2 1.5 1.7 1.9 2.0

f(x) 1 3 4 6 7 8 10

5. Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for the integral from 0 to 4 of x squared, dx.