### Second order homogeneous differential equation and power series.

Use power series to solve the second-order homogeneous equation : u''(t) - tu'(t) - 2u(t) = 0

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Use power series to solve the second-order homogeneous equation : u''(t) - tu'(t) - 2u(t) = 0

A particle of mass m moves under the influence of constant force f and the friction force γ(xdot)n Its equation of motion reads: m(x-double dot) + γ(xdot)n = f Find x(t) for n=1 and n=2 if x=0 and x-dot=0 at t=0 Check that your solutions exhibit the correct behavior in the limit. Please see the attac

4. Find the center, vertices and foci of 4x^2 + 9y^2 -8x +36y +4 =0. Graph, labeling all relevant points including the foci. 5. Find the equation of the hyperbola whose center is the origin, vertex at (2,0) and focus at (3,0). Write the equation of the asymptotes. 6. Find the center, vertices, foci and asymptotes

F(x,y)=1/(x^2+y^2) Is the domain (-infinity, 0) union (0, infinity)? Is the range (0, 1]? What are the x and y intercepts and is the z intercept undefined?

How do you find the x, y, and z-intercepts of a 3-Dimensional graph step by step? I am trying to interpret some graphs and would like this information to assist me in the interpretation. keywords: 3D, 3Dimensional

2. A spring with a 4-kg mass has natural length 1 m and is maintained stretched to a length of 1.3 m by a force of 24.3 N. If the spring is compressed to a length of 0.8 m and then released with zero velocity, find the position of the mass at any time t. 10. As in Exercise 9, consider a spring with mass m, spring constant k,

Find the length of an Archimedian spiral r=x, for 0<= x <= 2pi

Question: Derive the formula for the derivatives of the functions (1) x^n (2) x/(2x-3)

A box with its base in the xy-plane has its four upper vertices on the surface with equation z = 48 - 3x^2 - 4y^2 . What is the maximum possible volume.

Solve the differential equation using the method of variation of parameters. Solve the differential equation or initial-value problem using the method for undetermined constants. y''-4y=e^x cosx y(0)=1, y'(0)=2 y''+y'- 2y=x - sin 2x y(0)=1, y'(0)=0 y'' + y = cot x 0<x<pi/2 See attached file for full problem description.

Let h(t) = ln(t) +1. Determine the equation of the line that is tangent to the graph of h(t) at the point where t =3. Provide a graph of your work showing the function and the tangent line you are identifying. (Note: You may round all decimal values in this problem to the nearest thousandth.)

Solve the differential equations: a. 16y''+24y'+9y =0 b. 9y''+4y = 0 c. d2y/dt2 - 6 dy/dt +4y = 0

Using LaPlace Transforms Solve for currents I1 and I2; all currents and charges are 0 at t=0 E(t) = 2H(t-4) - H(t-5) See attached file for full problem description.

In system below spring k1 is anchored at the left side and has a spring constant of k1, spring K2 has a spring constant of k2; the system is not subjected to friction or damping. Block M is subjected to a periodic driving force f(t) = A sin(ωt). Both masses are initially at rest in the equilibrium position Using L

Two objects of mass M1 and M2 are attached to the opposite ends of a spring having a spring constant K; the entire apparatus is placed on a frictionless table. The spring is stretched and then released. Using Laplace transforms to solve the differential equations show that the period is: See attached file for full problem des

Find the Inverse LaPlace Transform using different methods described in the attachment. To see the description of the problem in its true format, please download the attached question file.

Find the inverse LaPlace Transforms from the attachment.

See attached file for full problem description. 1. cos(200*pi*t) 2. sin(200*pi*t) 3. sqrt(2) & cos(200*pi*t - pi/4) 4. If the signal above was written like this, can a time delay be applied??

Domain Interval Notation. See attached file for full problem description.

1) The terms of series are defined recursively by the equations: a1=2 a(n+1)=(5n+1)/(4n+3)an Determine whether ?" an converges or diverges 2) a) Show that ?" (from n=0 to infinity) [x^n/n!]converges for all x b) Deduce that lim ( n--> infinity)[x^n/n!] = 0 for all x

4. A hospital has seven large identical heat pumps. If one of the heat pumps malfunctions, it could seriously impact hospital operations. If preventive maintenance is performed weekly, it costs $1200 to perform preventive maintenance (PM) on all seven of them. If one of the heat pumps breaks down between PM inspections, the av

a) y'' - 5y' +6y = f(t) y(0) = y'(0) = 0 b) y'' - 8y + 12y = f(t) y(0) = -3 ; y'(0) = 2 Put solution in terms of f(t)

Y''' - 8y = g(t) y(0)=y'(0)=y''(0)=0 g(t) = 0 for t greater/equal to 0 and less than 6 g(t) = 2 for t equal to or greater than 6 Please solve using Laplace transforms

Find Y(t) fot all t = { 1 0 (less than or equal to) t (less than) Pi/2 Y'' + Y = f(t) f(t) = { 0 Pi/2 ( less than or equal to) t (less than) Infinity

Solve : Y''+Y = g(t) Y(0) = 0 Y'(0) = 1 { = t/2 0 (less than or equal to) t (less than) 6 g(t) { = 3 t (greater than or equal t

See attached file for full problem description. 1. First find a general solution of the differential equation dy 3y dx = . Then find a particular solution that satisfies the initial condition that y(1) = 4. 2. Solve the initial value problem dy y3 dx = , y(0) = 1. 3. Nyobia had a population of 3 million in 1985. Assum

1 .12y'' + 400y' + 25y = 120sin(20x) 2. .1y'' + 300y' + 167y = x*e^(-x) in both cases at x=0, t=0 and y' = 0 use undetermined coefficients to solve for a particular solution keywords: ODE, IVP

1. Solve the initial-value problems and graph the solutions on the same set of axes. y'' + 4y' + 2y = 0 y(0) = 5; y'(0) = 0 y'' + 4y' + 2y = 0 y(0) = 0; y'(0) = 5 2. Repeat problem 1 for the equation: y'' + 2y' + 5y = 0 y(0) = 5; y'(0) = 0 y'' + 2y' + 5y = 0 y(0) = 0; y'(0) = 5

Please see the attached file for the fully formatted problems. Includes: Solve the following inequalities/equations expressing the solution. Show all work and box the final answer. Write an equation for the line described below. Graph the following function. What symmetries, if any, does the graph have? Find the v

Susie is opening an online savings account with an interest rate of 5.5%, compounded continuously. She wants the account to have a balance of $4,000 after 6 years. Assuming the interest rate stays the same, how much money must Susie deposit now in order to reach her goal? (Show formula and answer in a complete sentence)