1. Estimate the differential equation: Estimate y(1) using a step size h=0.5 y' =y-x-1, y(0) = 1

At time t = 0, 5 grams of salt are dissolved into 15 liters of water. Brine with concentration of salt 4 grams per liter is added at a rate of 2 liters per minute. The tank is well mixed and drained at 2 liters per minute. Let ɩ be the Q amount of salt, in grams, in the solution after ₺ minutes t have elapsed. Find a differential equation for the rate of change in the amount of salt, dQ/at, in terms of the amount of salt in the solution Q. dQ dt grams/minute

The daily rate of change of the number of Pokémonin Brentwood is proportional to the square root of the number of Pokémon there are, minus the number of Pokémon hunters. (There are a fixed number of Pokémonhunters in Brentwood, say it’s 1000.) Write the differential equation that models this situation.

Most savings banks advertise that they compound interest continuously, meaning that the amount S(t) in an account satisfies the differential equation ds/dt=rS, where is the annual interest rate and t is time measured in years. Show that an annual interest rate of 8% compounded continuously is the same as an annual interest rate of 8.33% compounded in years.  Show that an annual interest rate of r compounded continuously is the same as an annual interest rate of e^r-1 compounded annually.

Find the second differential of the function y=x2cos2x.

The concentration of a medication M in mg/L present in the bloodstream decreases over time such that the concentration of medication is proportional to the amount of medication t hours after the first dose. The concentration of medication 30 minutes after the first dose is 80 mg/L and was decreasing at a rate of 150 mg/L per hour. Which differential equation represents this relationship? dM =-1.875M dt dM =-1.25M dt dM = -0.66M dt dM = -0.063M dt

What is the differential equation of the given functions?

Form the differential equation of family of lines situated at a constant distance p from the origin. Find the equation of the circle which touches both the axes and the straight line 4x + 3y = 6 in the first quadrant and lies below it

Morphine is administreted to a patient intravenously at a rate of 2.5 mg per hour. About 34,7% of the morphine is metabolized and leaves the body each hour. Write a differential equation for the amount of morphine, M, in milligrams, in the body as a function of time, t, in hours.

A certain drug is administered intravenously to a patient at the continuous rate of 10 milligrams per hour. The patient's body removes the drug from the bloodstream at a rate proportional to the amount of the drug in the blood. Select the differential equation that is satisfied by the amount f(t) = y of the drug in the blood at time t. Identify the graph of a typical solution. ... Select the correct differential equation. A. y' = 10k + y, k>0 В. у'%3D10 + ky, k0 D. y' = 10k + y, k<0 Select the appropriate graph of the solution to the differential equation. А. В. OC. D. Ay 6- Ay 4- AY 4. Ay 5- 2- 2- t 0- 10