### 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.

Explore BrainMass

- Anthropology
- Art, Music, and Creative Writing
- Biology
- Business
- Chemistry
- Computer Science
- Drama, Film, and Mass Communication
- Earth Sciences
- Economics
- Education
- Engineering
- English Language and Literature
- Gender Studies
- Health Sciences
- History
- International Development
- Languages
- Law
- Mathematics
- Philosophy
- Physics
- Political Science
- Psychology
- Religious Studies
- Social Work
- Sociology
- Statistics

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

1. Find a general solution of the differntial equation Then find a particular solution that satisfies the intiial condition . 2. A bacteria population is incresing according to the natural growth formula and numbers 100 at 12 noon and 156 at 1 p.m. Write a formula giving after hours. 3. Apply Euler's method to th

Assume An=[-1/6+ 1/(n+1), 1/(n+2). Calculate lim An or prove it does not exist.

Dy/dx=(-y^3 ) (x) (e^(-2x) + y) Please write the final answer explicityly in terms of y.

Water level in containers - Differential equations. See attached file for full problem description.

(See attached file for full problem description)

The function is defined by: erf(x) = for each x 1. Show that erf is strictly increasing on (- ,+ ) 2. Express the integral in terms of the values of erf. Hint(May want to do a substitution)

(See attached file for full problem description) Using the fundamental theorem of calculus and chain rule, For example, letting the expression equal F(x), and G(u) So for 1) we would have F(x)=G(x ) By the chain rule, dF/dx(x)=(dG/du)|u= x (du/dx) =(1/ | u=x ) (2x) =2x// Determine the derivative: 1) d/dx

Please see attached file for full problem description: Using the fundamental theorem of calculus and chain rule, For example, letting the expression equal F(x), and G(u) Determine the derivative:

1. find the solution of the initial-value problem: dy/dx = (sin(3x))/(2+cos(3x)), y=4 when x=0 using equation: (f'(x))/(f(x)) dx = ln(f(x)) +c (f(x) > 0) when integrating. 2. a. find in implicit form, the general solution of the differential equation: dy/dx = (4y^(1/2)(e^-x -e^x))/ ((e^x +

Bayside General Hospital is trying to streamline its operations. A problem-solving group consisting of a nurse, a technician, a doctor, an administrator, and a patient is examining outpatient procedures in an effort to speed up the process and make it more cost effective. Listed here are the steps that a typical patient follows

Instructions for this posting ? All calculations must be shown and all steps must be motivated. A correct answer without the necessary detailed explanation will not earn full marks. Therefore I will not accept the response. ? Please plot all graphs in MATLAB. If you do not have MATLAB then you may use Mathematica, Maple or Ma

Please see attached and show correct work.

Please see attached and show correct work.

See attached file for full problem description.

Describe a real world situation that could be modeled by a function that is increasing, then constant, then decreasing. What would be the difficulties associated with modeling this situation?

Hi, I need to find a formula for the sequence below by first finding a recurrence for a_n, then solving the recurrence. Thanks! a_n = 1/2 + 2/4 + 3/8 + 4/16 + 5/32 + · · · + n/(2^n) = sum_{k=1}^n (k /(2^k))

I need this solved using generating functions. Thanks! 2a_{n+2} − 3a_{n+1} − 2a_n = 25 à? 2^n, a_0 = 4, a_1 = −1

1. A function f(z) is said to be periodic with a period a, a is not equal to zero. if f(z+ma) =f(z), where m is an integer different from zero. prove that a function, which has two distinct periods say, a and b which are not integer multiples of the other- can not be regular in the entire complex plane. Note: Doubly p

1. A corporation manufactures a product at two locations. The cost of producing x units at a location one and y unites at location two are C1(x)=.01x^2 + 2x + 1000 and C2(y)=.03y^2 + 2y + 300, respectively. If the product sells for $14 per unit, find the quantity that must be produced at each location to maximize the profit P(

1. Sketch Graph: f(x) = 3x4-2x³-12x²+18x (MUST SHOW ALL WORK) 2. Sketch Graph: f(x) = x4-18x²+81 (MUST SHOW ALL WORK) Note: The 4 in both problems is an exponent

I need help doing two calculus problems #11, and #13. Each one is 5 parts (a,b,c,d,e) I have attached 3 files a) class notes for rectilinear motion b) the assignment (only problems 11 and 13) and my initial work on #11. I understand how to calculate 11 a, b, c but I get stuck on d, e. Can you explain what is going on and d

Suppose that y1, y2 are linearly independent solutions to the differential equation: a2 (x) y'' + a1 (x) y' + a0 (x) y = 0. a) Show that a2 (y1 y2'' - y2 y1'') + a1(y1 y2' - y1' y2) = 0 b) show that (a) implies a2 W' + a1 W = 0 {here W means the Wronskian) c) show that the equation in (b) implies W

3. Write the first four terms of the defined sequence a lower case 1 = 1 a lower case n=na lower case n-1, n>1 9. Write the following in summation notation 3+6+9+12+15 10. Write the following in summation notation: x+x^2/2 + x^3/6 + x^4/24 14. Find the fifth term in the expansion of (a + b)^16 15. Write the bi

Use a power series method to find the solution of x^2 y'' + 2xy' + 4y = 0 that is valid in any interval not including the singular point. y=0 is a trivial solution which exists for any linear Homogeneous equation. So it is correct but absolutely not enough to complete the problem. Since the equation is linear and has non

A relation between a function f(x) and its derivative f'(x) = x√f(x) is given with an initial condition on f(x) as f(4)=16. One needs to find the value of the second derivative of the function i.e., f"(4). Also an expression to f(x) in terms of x is to be evaluated. Please see the attached file for the fully formatted

Sketch the following function f(x) = -x³ + 3x² + 9x +5

Consider the differential equation (dy/dx) = (-xy^2)/2. Let y=f(x) be the particular solution to this differential equaiton with the initial condition f(-1)=2. a) On the axis provided sketch a slope field for the given differential equation t the twelve points indicated. (the x-axis goes from -1 to 2 and the y-axis goes from