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Calculus and Analysis

Use reduction of order to find a second solution to a differential equation.

Given that y1(x)=e^-x is a solution of y'' + 2y' + y =0, find second solution using the method of reduction of order. I substituted y =ve^-x so y' = v'e^-x - v^-x; y''= v''e^-x -v'e^-x +v e^-x I came out of that with v''e^-x + v'e^-x =0 I think the next step is to seperate variables. Looking for help to finish the pro

Average Rate of Population Increase

In April 1990, the population of Phoenix was 983,403. In April 2000, the population of Phoenix was 1,321,045. What was the average rate of increase in population per year?

Limit using epsilon delta defintion

Show that: lim (x+y)=o as x and y approach zero; using the epsilon-delta definition Also, show that: lim f(x)=1 as x approaches zero; using the epsilon-delta definition. **Note: x is a vector in this case, with a right arrow going over it. It is not just "x".

Linear differential operator

Problem states " if L[y] =ay'' +by' +cy, where a,b,and c are constants, compute L[e^rx], where "r" is constant. Is this just a matter of substituting for "y"? Please work out, thanks!

Solving for the Given Limit

Please see the attached document to view this problem formatted properly. Evaluate the limit: lim 1/(x - 2) x --> 2


Please see the attached file for the fully formatted problems.

Evaluate the Given Limit

Please see the attached file for proper formatting. Evaluate the limit: lim 1/x x --> - inf. Include all steps required for solving.

Modeling with Higher Order Differential Equations

Two springs are attached in series as shown in Figure 5.42. If the mass of each spring is ignored, show that the effective spring constant k ot the system is defined by I/k = I/k + I/k2. A mass weighing W pounds stretches a spring 1/2 foot and stretches a different spring 1/4 foot. The two springs are attached, and the mass is

Differential Equation and Initial-Value Problem

In Problem 42 solve the given initial-value problem in which the input function gx) is discontinuous. (Hint: Solve each problem on two intervals, and then find a solution so that v and y' are continuous at x = pi (Problem 42).) 42. y" ? 2y' + 10y= g(x), y(O) = 0, y'(0) = 0, where g(x)={20 0<x<pi {0 x>pi

Laplace initial value

(See attached file for full problem description) Solve initial value problem y(0)= -3

An open-top box is to be made as follows...

(See attached file for full problem description with diagram) An open-top box is to be made as follows: squares of a certain size will be cut away from each of the four corners of a 20" x 30" rectangle, and the ends will be folded upward to form the corner seams, as shown. How big should the square cutouts be in order to maxi

Reduction Formula

Please show problem step by step I need very detailed info so I can memorize steps for upcoming quiz. Scanned work is ok as long as I can read it. y''- 4y =2; y1= e^(-2x). See attached file for full problem description.

Power Series Method

1. Use the power series method to solve the following initial value problem (other methods are not acceptable) xy" ? xy' + y ? = 0, y(0) = 1, y'(0) = 2. Your answer must be in closed from. That is, your answer must not have infinitely many terms. Remember that you MUST show all work. 2. Find the general solution of the diffe