### Cartesian and Polar Forms and Cauchy-Riemann Equations

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Please see the attached file for the fully formatted problems.

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

Determine the number of units x for which marginal revenue is equal to marginal cost. R(x) = 240x - 0.02x2 C(x) = 210x

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?

Use implicit differentiation to find an equation of the line tangent to the curve x^3+2xy+y^3 = 13 at the point (1,2).

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".

Let G(x) = Int(0..x, (Int(0..s, f(t)dt)) , ds), where f is continuous for all real t. Find a) G(0) b) G'(0) c) G''(x) d) G''(0)

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!

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.

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

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

(See attached file for full problem description)

Prescribed text: Viscous fluid flow by Frank White (See attached file for full problem description)

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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

(See attached file for full problem description) f(x)=x+[|x^2|]-[|x|]

Please see attached file for full problem description. As you can see I understand the format but not how to substitute the values from the original equation and then simplify.

(e^x+1) dy/dx=y-ye^x Problem is separable, solve for "y"

(See attached file for full problem description) I have one question and I am looking for an accurate answer with full working (and diagrams if necessary).

(x+e^y)dy-dx=0 This is linear in "x". Can you show how it is integrated to the proper answer?

D2y/dt2 - 4 dy/dt = 6 e^3t -3e^-t y(0)=1 y'(0)-1

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

(See attached file for full problem description)

A mass of 25g is attached to a vertical spring with a spring constant k = 3 dyne/cm. The surrounding medium has a damping constant of 10 dyne*sec/cm. The mass is pushed 5 cm above its equilibrium position and released. Find (a) the position function of the mass, (b) the period of the vibration, and (c) the frequency of the v

(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

Differential Equations. See attached file for full problem description. There are two problems 20,27

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.

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

D2y/dx2- dy/dx - 4y =0