Differential Equations: Find the general solution by using infinite series centered at a.

4.xy′′+ y′− y = 0, a=0.

Differential Equations: Find the general solution by using infinite series centered at a.

2. (x² +1)y′′ + xy′ + y = 0, a=0.

Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces at the given point. (Enter your answers as a comma-separated list of equations.) z = sqrt(x2 + y2) , 9x − 3y + 5z = 40, (3, 4, 5)

Consider a nonhomogeneous differential equation

?′′ + 2?′ + ? = 2? sin?

(a) Find any particular solution ?? by using the method of undetermined coefficients.

(b) Find the general solution.

(c) Find the particular solution if ?(0) = 0 and ?′(0) = 0.

My instructor doesn't have the most intelligible answer keys. Could you explain how to solve this?

Math 266, Quiz 15: Answers due today, April 22, by 1:00 PM via email.

1. Let g(t) be given by

?(?) = {

0, 0 < ? < 1

? − 1, 1 < ? < 2

3 − ?, 2 < ? < 3

1, ? > 3

Rewriting ?(?) using the unit step function gives:

a) ?(?) = (? − 1)?(? − 1) + (4 − 2?)?(? − 2) + (? − 2)?(? − 3)

b) ?(?) = (? − 1)?(? − 1) − (? − 1)?(? − 2) + (? − 3)?(? − 2) − (? − 3)?(? − 3) + ?(? − 3)

c) ?(?) = (? − 1) − (? − 1)?(? − 2) + (3 − ?)?(? − 2) − (3 − ?)?(? − 3) + ?(? − 3)

d) ?(?) = (? − 1)?(? − 1) + (1 − ?)?(? − 2) − (? − 3)?(? − 2) + (? − 3)?(? − 3)

e) None of the above.

2. Use Laplace transforms to solve ?′′ + ? = ?(? − 1) − ?(? − 2) with ?(0) = 0, ? ′ (0) = 1

If an undamped spring-mass system with a mass that weighs 6 lb and a spring constant 9 lbin is suddenly set in motion at t=0 by an external force of 33cos(20t) lb, determine the position of the mass at any time. Assume that g=32 fts2. Solve for u in feet.

Enclose arguments of functions in parentheses. For example, sin(2x).

u(t)=?

Solve the non-homogeneous DE: y'' + 2 y' = e^t+ 3 using undetermined coefficients

Differential Equations: Find the general solution by using infinite series centered at a.

3. y′′ + (x+1)y′ − y = 0, a=−1.

In your Solutions to Pinters a Book of Abstract Algebra Chapter 8 Exercise H3 i can not understand in step 5 you get (ab)(cd)=(dac)(abd). Can you show me in some detail how to get that result please?

Calculate the integral of the function f (x, y, z) = xyz on the region bounded by the z = 3 plane from the bottom, z = x ^ 2 + y ^ 2 + 4 paraboloid from the side, x ^ 2 + y ^ 2 = 1 from the top.

1. Find the general solution to the following ODE:

y′′′+ 4y′= sec(2x)

2. Find the solution to the following IVP:

2y′′+ 2y′−2y= 6x²−4x−1

y(0) = −32

y′(0) = 5

3. Verify that y₁=x^1/2ln(x) is a solution to

4x²y′′+y= 0,

and use reduction of order to find a second solution y₂.

4.

Find the general solutions to the following ODEs:

a) y′′′−y′= 0.

b) y′′+ 2y′+y= 0.

c) y′′−4y′+ 13y= 0.

For the following Linear Programming problem, use the Simplex Approach to construct the starting simplex tableau:

Maximize ???? = P = 4 X + 5 Y

Subjected to: 3 X + 5 Y ≤ 20

X + Y ≤ 6

X, Y ≥ 0

Then apply Gauss-Jordan computations to determine the new basic solution and find the Optimum Solution?

1. Given f(x) = exp x sinx. Find exact first derivative at x = 1.0. In addition, find approximate first derivative using forward, backward, central and higher order scheme for first derivative. Set h = 0.1 for approximation.

2. Given f(x) = xlnx. Find exact and approximate second derivatives at x = 1.0. Set h = 0.1 for approximation.

3. Develop a 4th order accurate symmetric scheme to approximate the second derivative of f(x) at x.

solve the equation:

y''-8y'+25y=5x³e^-x - 7e^-x