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How a second order differential equation can be used

Assignment Help Electrical Engineering
Reference no: EM131420897

ASSIGNMENT OBJECTIVES

In this assignment, for the Pass criteria, you will need to show that you can:

L04.1 Analyse problems using first order differential uations

LO4 2 Solve first order differential equations using a range of techniques

LO4 3 Understand how second order differential equations arise in engineering contexts

L04.4 Solve second order differential equations

L04.5 Use first and second order differential equations in engineering situations

For the Merit criteria, you will need to achieve the Pass criteria above and show:

Task 1

You must answer both parts (a) and (b) Your work colleagues; who recently left the company have created a number of differential equations after running some simulations. Your task is to help recreate the original equation in that describes the relationship of y with respect to x, that these are derived from.

(a) L04.2

(b) L04.1

Solve the following differential equation by direct integration:

(i) dy/dx = 4 + 3x2 dx

Solve the following by separation of variables:

(ii) dy/dx = 2y2 (iii) dy/dx = 3x2e-y (iv)dy/dx = 1/2y

(v)dy/dx = 2x/y (vi) dy/dx = 2x(y +1)

(b) After analysis of rock samples a scientific experiment yields a relationship modelled by the following equation:

dy/dx + 2y = e-x

Solve this equation using an appropriate method with which you are familiar to find an expression for y in the same way.

Task 2

(a) Using Internet, books, or by drawing upon learning from other units, explain (with a short example) how a second order differential equation can be used as a mathematical model in an engineering context.

(b) As a result of some research on pressure differentials on certain strata of rock material, it is required to solve the differential equation below.

Given that that y=2 and dY/dx = 4 at x=0 solve the following differential equation using an appropriate method.

d2y/dx2 = 3

Verified Expert

In task 1 we have solved the differential equation by direct integration and by separation of variables. And also a problem or given differential equation is solved by the laplace transformation. In task 2 we a note on "a second order differential equation can be used as a mathematical model in engineering context - vibration spring and electrical circuit" is discussed. and finally a differential equation by the laplace transformation is solved.

Reference no: EM131420897

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Reviews

inf1420897

3/20/2017 4:24:43 AM

Very good work. Much obliged to you for rolling out the improvements after I ask for update from the expert! Thanks to you for the nature of client administration that you give.

len1420897

3/9/2017 5:09:32 AM

Opportunities for Higher Grading In this task you may gain D3 by showing evidence of effective thinking by using the correct technique to solve the equation, and furthermore, a method to check your solution. You have not been shown a checking method in class, but should be able to refer to previous learning in a different situation to help you choose an appropriate method.

len1420897

3/9/2017 5:08:27 AM

Have used critical reflection to evaluate your work and justify your conclusions Task 2 requires you to demonstrate effective thinking by checking your solution using other techniques. You may have learned these skills in evious mathematics units.

len1420897

3/9/2017 5:08:13 AM

Analyse problems using first order differential uations Solve first order differential equations using a range of techniques Understand how second order differential equations arise in engineering contexts Solve second order differential equations Use first and second order differential equations in engineering situationsYou have independently applied strategies to find appropriate solutions to problems You have independently designed/selected/applied appropriate methods/techniques to produce solutions to problems You have presented and communicated your findings appropriately/fully/professionally

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