Find the general solution of this ODE: d²y dy +18- +81y = -e-⁹t dt² dt The solution will be of the form: y(t) = Cyi(t) + Dy2(t) + yp(t)

The population Pinmillions of Texas from 2001 through 2014 can be approximated by the model P=20.913e0.0184t, where t represents the year, with t=1 corresponding to 2001. According to this model, when will the population reach 32 million?

Does the equation y=2.294e0.654t representcontinuous growth, continuous decay, or neither?Explain.

The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?

ACT6.4 FIND THE GENERAL SOLUTION

Water containing 0.5 lb/gal of salt enters a tank at a rate of 2 gal/min and leaves the tank at a rate of 3 gal/min. Suppose the tank initially contains 300 gallons of water and 60 lb of salt. (a) Set up an ODE for the amount of salt in the tank, x(t). b)solve it c)Sketch an accurate solution for x(t). Don't omit details.

dx x(2x+1) S-

A person's Body Mass Index is I = 2, where W is the body weight (in kilograms) and H is the body height (in meters). W H² Estimate the change in height that will decrease I by 1 if (W, H) = (26, 1.3), assuming that W remains constant. (Use decimal notation. Give your answer to three decimal places.) AH≈