Differential Equations

Find the general solution of the following differential equations

A very large tank initially contains 100L of pure water. Starting at time t=0 a solution with a salt concentration of 0.7kg/L is added at a rate of 6L/min. The solution is kept thoroughly mixed and is drained from the tank at a rate of 4L/min. Answer the following questions.1. Let y(t) be the amount of salt (in kilograms) in the tank after t minutes. What differential equation does y satisfy? Use the variable y for y(t).Answer (in kilograms per minute): dydt =

The differential equation below models the temperature of a 95°C cup of coffee in a 21°C room, where it is known that the coffee cools at a rate of 1°C per minute when its temperature is 71°C. Solve the differential equation to find an expression for the temperature of the coffee at time t. (Let y be the temperature of the cup of coffee in °C, and let t be the time in minutes, with t = 0 corresponding to the time when the temperature was 95°C.) dydt = − 150(y − 21)

differential equations to linear algebra using matrices

In Problems 19 and 20 verify that the indicated expression is an implicit solution of the given first-order differential equation. Find at least one explicit solution y (x) in each case. Use a graphing utility to obtain the graph of an explicit solution. Give an interval I of definition of each solution ./frac (dX)(dt)= (X -1)(1- 2X); ln /frac (2X- 1)( X -1)