Connected Graphs

Let G be a connected graph in which for every edge there are cycles C1 and C2 both containing e while no other edge share by C1 and C2 . Prove that G is 3-edge-connected.

Double Integrals : Disk Integral

Suppose that where D is the disk . Now suppose E is the disk and . What is the value of ?

Ordinary Differential Equations : Solving Initial-Value Problems

2. Solve the initial-value problem a. 2y’’+5y’-3y =0 , y(0) =1, y’(0) =4 b. y’’-2y’+5y =0 , y(pi) =0, y’(pi) = 2 c. y’’+12y’+36y = 0 , y(1) = 0, y’(1) = 1 keywords: IVP

Differential Equations : Solving Boundary-Value Problems

3. Solve the boundary-value problem, if possible. a. y’’-6y’+9y =0, y(0) =1 and y(1) = 0 b. 9y’’-18y’+10y = 0 , y(0) =0 and y(pie) = 1 4. If a, b and c are all positive constants and y(x) is a solution of the differential equation ay’’+by’+cy = 0, show that lim x->infinity y(x) = 0

Integrating Differential Equations

1. Consider the following differential equation: (1-c/r)(dt/dl)2 - (1-c/r)-1(dr/dl)2 = 0 (a) Show that this equation can be written as dr/dt = (1-c/r) (b) Solve the above equation for t(r). Please evaluate integrals by hand. Take c to be a constant Please see the attached file for the fully formatted proble ...continues

Differential Equations

Find the general solution of the following (d^6y/dx^6) -3*(d^4y/dx^4) +3*(d^2y/dx^2) -y=0

Higher order differential equation

Find the general solution to the following (d^4y/dx^4) + 4(d^3y/dx^3) + 8(d^2y/dx^2) + 8(dy/dx) + 4y=0

Derivatives, Tangent Lines and Rates of Change

1. A curve has the equation x²-4xy+y²=24 a) Show that dy/dx= (x-2y)/(2x-y) b) find the equation for the tangent to the curve at the point P (2, 10) The tangent to the curve at Q is parrallel to the tangent at P c) find the coordinates of Q 2. The diagram shows the coss-section of a vase. The volume of the water in th ...continues

Differential Equations : Composite Functions and the Chain Rule

Chain Rule. See attached file for full problem description.

Solving Inseparable Differential Equations

Consider the following very simple model of blood cholesterol levels based on the fact that cholesterol is manufactured by the body for use in the construction of cell walls and is absorbed from foods containing cholesterol: Let C(t) be the amount (in milligrams per deciliter) of cholesterol in the blood of a particular person a ...continues