Differential Equations Answers

Suppose that 𝑑𝐴 𝑑𝑡 = −0.0004332 𝐴(𝑡) represents a mathematical model for the radioactive decay of radium – 226, where 𝐴(𝑡) is the amount of radium (measured in grams) remaining at time 𝑡 (measured in years). How much of the radium sample remains at the time 𝑡 = −0.002 with initial condition 𝐴(1) = 0.005

Consider a flask that contain 3 liters of salt water. Suppose that water containing 25 grams per liters of salt is pumped into the flask at the rate of 2 liters per hour, and the mixture, being steadily stirred, is pumped out of the flask at the same rate. Find a differential equation satisfied by the amount of salt 𝑓(𝑡) in the flask at time 𝑡.

form the partial equation by eliminating the function f from z=f(y/x)

The rate at which a super computer body cools is proportional to the difference between the temperature of the body and that of the surrounding air. If a body in air at 25°C will cool from 100°C to 75°C in one minute, find its temperature at the end of three minutes.

Find the general solution using D-operator

(D + 4)^2x = sihn4t

The population of a city increases at a rate proportional to the present number. It has an initial population of 50000 that increases by 15% in 10 years. What will be the population in 30

years?

Given an example of an elliptic partial differential equation of 2nd order,

justifying your answer

Under certain conditions, orange is converted into juice at a rate, which is proportional to the

amount unconverted at any time. If out of 70 grams of juice at t = 0, 6 grams are converted

during the first 3 minutes, find the amount converted in 1.5 hours.

Solve the homogeneous differential equation 𝑥𝑦 𝑑𝑦/𝑑𝑥 = 𝑦² + 𝑥² 𝑑y/𝑑𝑥   .