### Differential Equations : Variation of Parameters

Use variation of parameters to solve the differential equation y'''+4y'=cot2t.

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Use variation of parameters to solve the differential equation y'''+4y'=cot2t.

1.) Decribe the region R in the xy-coordinate plane that corresponds to the domain of the function. f(x,y)=e^x/y Decribe the region R in the xy-coordinate plane that corresponds to the domain of the function. 2.) f(x,y)=sq rt 9-9x^2-y^2 3.) f(x,y)=x/y

Trouble finding the power series to resolve the question.

36. A holding tank has the shape of a rectangular parallelepiped 20ft by 30ft by 10 ft. a) How much work is done in pumping all the water to the top of the tank? b) How much work is done in pumping all the water out of the tank to a height of 2ft above the top of the tank? Please see the attached file for all nine questions

Consider the diffusion equation ut = ku.xx for 0 < < pi and t > 0 with the boundary conditions ux(0, t) = 0 and u(pi, t) = 0 and the initial condition u(x,0) = 1. (a) Find the separated solutions satisfying the differential equation and boundary conditions. (b) Use these solutions to write an explicit series solution to t

How did the book get from here: -2X(1+x^2)^2 - 4X(1-x^2)(1+x^2) ______________________________ (1 + x^2)^4 to here? -2x (1+ x^2)[1+x^2+2(1-x^2] ___________________________ (1+x^2)^4 I have worked and reworked and I cannot get that numerator to become that. What is the deal? (This

A high-tech company purchases a new computing system whose initial value is V. The system will depreciate at the rate f=f(t) and will accumulate maintenance costs at the rate g=g(t), where t is the time measured in months. The company wants to determine the optimal time to replace the system. a) Let C(t)=1/t the integral fr

Let x=1 and delta x= 0.01, find delta y. f(x)=5x^2 - 1 f(x)=sq rt 3x compare the values of dy and delta y y=x^3 x=1 delta x=dx=0.1 y=x^4+1 x=-1 delta x=dx=-0.1 Part 2 Use differentials to approximate the change in cost , revenue, or profit corresponding to an increase in sales of one

Questions: 4,6,10,12,18,22,26,30,34,36,42,44,46,48,50 on page 6.3. 2,8,22,14,18,12,24 on page 393 4. Identify each of the curves as a cardinoid, rose curve (state number of petals), lemniscate, limacon, circle, line of none of the above. Please see attached for all questions.

Problems: 2, 6, 8, 12, 14,16,18,20,and 22, 28 done. Page 372: 2, 6,10,14,16,20,22,24,26,28,32,34 done. 28. Find the area of the region that contains the origin and is bounded by the lines 2y = 11 - x and y = 7x + 13 and the curve y = x² - 5. Please see attached for full question.

Evaluate the limit by first recognizing the sum as a Riemann sum of a function: the limit as n goes to infinity of (4/n)(sqrt(4/n)+sqrt(8/n)+...+sqrt(4n/n))=___

Problem 9.1 (Prob. 29. P. 252) Two particles each of mass m moves in the plane with co-ordinates (x(t), y(t)) under the influence of a force that is directed toward the origin and had magnitude k/(x2 + y2) an inverse-square central force field. Show that mx''=-kx/(r^3) and my''= -ky/(r^3) where r = sqrt(x2 + y2) Problem 9.2

1. Find a Particular Solution using undetermined coefficients, then find a general solution y³ + y" - 6y' = 3e²ⁿ. 2. Find a particular solution using the method of variation of parameters then find a general solution y" + 9y = cos(3x). 3. Solve the Initial Value Problem x" + 4x = 6sin(3t). x(0)=4, x'(0) = 0. Ple

Find the work done by the force field F(x,y,z)=... on a particle that moves along the helix... Please see the attached file for the fully formatted problems.

A motorist, in a desert 5 km from point A, which is the nearest point on a long straight road, wishes to get to point B on the road. If the car can travel 30 km/ hr and 80 km/hr on the road, find the point where the motorist must meet the road to get to point B in the shortest possible time if point B is 5 km from point A. Use c

Please assist me with the attached problems, including: 1. Find the dot product 2. State whether the given points of vectors are orthogonal 3. Evaluate the expressions

I need some clues on figuring out these questions. Please see attachment for complete problems (regarding the below: "..." indicates an equation to be found in the attachment. Thanks!) (a) Using polar coordinates, find all the separated solutions of Laplace's equation satisfying the attached boundary conditions in the "wedge

What is it's origin? State the problem with picture. Explain how the cycloid relates to the solution.

Hi, I'm having trouble figuring out how to solve this. I think I figured out some of it, but I don't understand it in general. I attached the problem as a jpeg. I'd appreciate seeing how to show the answer. You can ignore the pencil markings, they are notes to myself in trying to figure out the problem. Thanks.

Find the average rate of change of the function over the indicated interval. Than compare the average rate of change to the instantaneous rate of change at the end points of the interval. f(x)= x^2 + 3x - 4; (0,1) The annual revenue R (in millions of $ per year) of Wm. Wrigley Jr. Company for the years 1994-2000 can

A. Find the general solution to the attached system of differential equations. x' = y y' = 2x b. Draw the phase portrait for this system and describe in words what happens to the solution for all initial conditions: x(0) = x0 and y(0) = y0

Solve, subject to the given initial conditions: x(0) = x'(0) = 0 solve x'' + x = sec t t ε (-pi/2, pi/2)

Hi, I have worked this problem, but want to know if I did it correctly. If I did not do it correctly I would like to see how to do it. Attached is the problem and my answer. Thanks

Background Information: The paddles of a defibrillator in an ambulance or the emergency room of a hospital are actually the two plates of an electronic device called a capacitor. A capacitor is built from two conducting plates that are attached to a voltage source. Due to the voltage source, electrical charges move through

Solve the differential equation for absolutely integrable (on R) solutions (See attached for equation)

Please see the attached file for full problem description. --- 1. A solid is bounded by two bases in the horizontal planes z = h/2 and z = -1/2, and by such a surface that the area of every section in a horizontal plane is given by a formula of the sort Area = a0 z3 + a1 z2 + a2 z + a3 (where as special cases some of

The effectiveness of E (on a scale from 0-1) of a pain killing drug t hours after entering the bloodstream is given by E= 1/27(9t+3t^2-t^3) o< or = t < or = to 4.5 Find the average rate of change E on the indicated intervals and compare this rate with the instantaneous rates of change at the end points of the intervals a.) [

3.) A company determines that the cost in dollars to the manufacture x cases of the dvd "math caught in embarrassing moments" is given by C(x) = 100 + 15x - x^2, (0< or = x < or = 7) a.) Find the average rate of change of the cost per case for the manufacturing between 1 and 5 cases [ review ex. 2a] So on the average,

Analyse and then plot the following curve: y = x^2 + 2x - 3

Please see the attached. The fundamental solution of the n-dimensional Laplace equation solves , (1) where is the n-dimensional delta function. a. Show that if , the solution of the above equation (1) for is , where is a constant. b. Use the n-dimensional Gauss theorem to evaluate the