Compute the laplace transforms of given functions

Assignment Help Engineering Mathematics

Reference no: EM131080772

1. Solve the following differential equations:

A. D (D + 3)³ (D² +9)(D²-2x-8)y = 0
B. y^m -4yⁿ-9y'+36y =0
C. y^m -4y' = x + 3 cos x + e^-2x [Hint: Use undetermined coefficients]
D. yⁿ +4y' +4y = x^-2e^-2x with x > 0 [Hint: Use variation of parameters]

2. Determine an annihilator for x² e^3x + 5 cos 2x.

3. Convert the following system to a first-order system:

d²x/dt² -3dy/dt+x = sint, d²y/dt² -tdx/dt-e'y=t²

4. Solve the following linear system of differential equations:

x₁' = x₁ + 2x₂
x₂' = 4x₁+ 3x₂

5. Solve the following nonhomogeneous linear system of differential equations:

x₁' = x₁ + 2x₂ +12e^3t
x₂'= 4x₁ + 3x₂ +18e^2t

6. Compute the Laplace transforms of the following functions:

A. e^5t sin 3t
B. u₂ (t)sin (5 (t - 2))

7. Compute the inverse Laplace transforms of the following functions:

A. 7e^-2s/s2 +4

B. 3s+2/ (s -1)(s -2)

8. Solve the following initial-value problem by using Laplace transforms:

yⁿ -4y =12e^2t with y(0)=2 and y' (0) = 3.

Reference no: EM131080772

Questions Cloud

Calculate and display the water bill : Write a Python program to determine how much a customer needs to pay. Ask the user how much water he has used. Calculate and display the water bill. The following are two examples.

For what does the case acronym stand : For what does the CASE acronym stand? In general, what is the purpose of CASE tools? What types of individuals are most likely to use CASE tools?

Categories of personal productivity software packages : List at least five categories of personal productivity software packages. Then concentrate on one of these categories, and describe a representative product in that category with which you are somewhat familiar.

Capability and features of three well-known nms : This week, you will prepare a research report summarizing the capability and features of three well-known NMSs.

Compute the laplace transforms of given functions : Determine an annihilator for x2 e3x + 5 cos 2x. Convert the following system to a first-order system: d2x/dt2 -3dy/dt+x = sint, d2y/dt2 -tdx/dt-e'y=t2

Complete binary tree : Assume that the binary tree from Question (a) above is stored in an array-list as a complete binary tree as discussed in class. Specify the contents of such an array-list for this tree.

Explain how given news media statement can impact a company : Briefly explain and discuss how the following news media statement can impact a company: "Venture Furniture failed to meet its second quarter earnings estimates. Venture stock fell by 10% in trading today."

What is southwest airlines doing to maintain the advantage : What is Southwest Airlines doing to maintain a competitive advantage? Who are their stakeholders and what are they doing to satisfy them? Why would someone be willing to work for Southwest at a lower pay than the market average?

Write a summary on this social psychology research : -describe the study's purpose (hypothesis or research question explored) -Describe the type of research conducted (experimental, correlational, quasi-experimental, etc.)

User Account

All Pages