Differential Equations and Rate of Change

A tank contains 54 gallons of pure water. A salt water solution with 2 pounds of salt per gallong enters the tank at a rate of 3 gallons per minute, and the well-stirred mixture leaves the tank at the same rate (3 gallons per minute). a. How much salt is in the tank at any time t? b. When, to the nearest minute, will the wat ...continues

Differential Equations and Rate of Change

A tank initially contains 100 gallons of a solution that holds 10 pounds of a chemical. A solution containing 1 pound of the chemical runs into the tank at a rate of 4 gallons per minute, and the well-mixed mixture runs out of the tank at a rate of 6 gallons per minute. a. How much chemical is in the tank after 25 minutes? b ...continues

Differential Equations : Electromotive Force and Maximum Current

An electromotive force of 100 volts is in series with a 2 henry inductor and a 50m ohm resistor. a. Determine the current i at any time t after the switch is closed b. Determine the maximum current that can be obtained in the simple circuit described. Please see the attached file for the fully formatted problems.

Differential Equations : LRE and CRE Circuits

A 20 ohm resistor, a .05 farad capacitor, and an alternating power source equal to 40 cos(t) are placed in series. If the initial charge on the capacitor is 3 coulombs, find a general formula for the charge at any time t.

Applications of Differential Equations : Mechanics

A perfectly flexible cable hangs over a frictionless peg as shown, with 8 feet of cable on one side of the peg and 12 feet on the other. The goal of this problem is to determine how long it takes the cable to slide off the peg, starting from rest. (a) At time t 0 what proportion of the whole cable is on the left side of the peg ...continues

Cable hanging on a peg

The problem involves a picture, so I am attaching the whole thing as a picture and as a .pdf document.

Basis and Dimension, Eigenvalues and Eigenvectors and Diagonalizability

Text Book: - Linear Algebra, Author: - Insel, 3rd Edition Following questions to be answered In page Number: - 52 & 53 : Questions: - 12, 21 In Page Number :- 54 :- Question :- 25 In page Number: - 247 :- Question : - 2 / c, d In Page Number: - 248 & 249 : - Question: - 3/ b,c. 4, 8/a, 11/a, b. 12/a In Page ...continues

Differenetial Equations and the Lanchester Combat Model : Solutions and Phase Portraits

Please see the attached file for the fully formatted problems.

Differential Equations

1. Solve: x*(dy/dx) - y = 2(x^2) * y 2. General solution for: dy/dx = ((x^2) + 1)/(2 - y) then particular solution for y = 4, x = - 3

First Order Differential Equations and Values of Parameters

Please see the attached file for the fully formatted problems. 1. Given satisfying , ; π ; find 2. Given such that , ; list all possible solutions. For which of these does ?; ? 3. Suppose for it is known that Where “a” is a parameter. Determine the value of this parameter which ensure the existence ...continues