Download presentation

Presentation is loading. Please wait.

Published byGlen Herod Modified over 3 years ago

1
Shortcuts: Solution by Inspection for Two Special Cases A Lecture in ENGIANA AY 2014 – 2015

2
Solution by Inspection It is frequently easy to obtain a particular solution of a non-homogeneous equation by inspection.

3
Special Case 1: R(x) = R 0, b n 0 For example, if R(x) is a constant R 0 and if b n 0, is a solution of because all derivatives of y p are zero.

4
Special Case 2: R(x) = R 0, b n = 0 Suppose that b n = 0. Let D k y be the lowest-ordered derivative that actually appears in the differential equation. Then the equation may be written

5
Special Case 2: R(x) = R 0, b n = 0 Now D k x k = k! is a constant, so that all higher derivatives of x k are zero. Thus, it becomes evident that is a solution of

6
Examples: Find a particular solution by inspection. 1)(D 2 + 4)y = 12 2)(D 2 + 4D + 4)y = 8 3)(D 3 – 3D + 2)y = -7 4)(D 2 + 4D)y = 12 5)(D 3 + 5D)y = 15 6)(D 4 – 4D 2 )y = 24 7)(D 5 – D 3 )y = 24

7
Solution to finding a particular solution by inspection. 1)(D 2 + 4)y = 12y p = 12/4 = 3 2)(D 2 + 4D + 4)y = 8y p = 8/4 = 2 3)(D 3 – 3D + 2)y = -7y p = -7/2 4)(D 2 + 4D)y = 12

8
Examples: Find a particular solution by inspection. 5)(D 3 + 5D)y = 15 6)(D 4 – 4D 2 )y = 24 7)(D 5 – D 3 )y = 24

Similar presentations

OK

The Rational Zero Theorem The Rational Zero Theorem gives a list of possible rational zeros of a polynomial function. Equivalently, the theorem gives all.

The Rational Zero Theorem The Rational Zero Theorem gives a list of possible rational zeros of a polynomial function. Equivalently, the theorem gives all.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on needle stick injury images Ppt on summary writing worksheet Ppt on carbon and its compounds class Ppt on hydraulic free piston engines Jit ppt on manufacturing jobs Sap procure to pay ppt online Ppt on data collection methods Ppt on symbols of elements Download ppt on indus valley civilization culture Ppt on current indian economy