{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

By Inspection - Silva Alviso and Llacuna – Mathematics...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Differential Equations Second Quarter SY 0506 ____________________________________________________________________________________________________________ Silva, Alviso and Llacuna – Mathematics Department, MIT 155 Lesson 30 By Inspection glyph1197on-Homogeneous Equation 4. Inspection It is easy to obtain a particular solution of a non–homogeneous linear differential equation by inspection if R(x) is a constant, R 0 . Standard Form: ( ) ( ) + + + + + = 1 2 0 1 2 1 ... n n n n n a D a D a D a D a y R x Case I. if n o p n a R y then a = , 0 Case II. if k n k o p n a k x R y then a = = ! , 0 Where: R 0 = constant found on the right side of the equation a n = constant term a n–k = coefficient of the lowest–ordered derivative k = lowest–ordered derivative Example: Find the particular solution of the differential equation. 2 5 5 , 2 5 ) 2 .( 2 3 4 12 12 , 4 12 ) 4 .( 1 2 2 = = = = = = = = = + p o n p p p o n p y R a y D D y y R a y D
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Differential Equations Second Quarter SY 0506 ____________________________________________________________________________________________________________
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Silva, Alviso and Llacuna – Mathematics Department, MIT 156 3 3 3 3 3 5 2 3 54 81 ) 9 )( 3 )( 2 )( 1 ( 81 ) 9 ( ! 3 81 9 , 3 , 81 , 81 ) 9 .( 3 x y x y x y x y a K R a y D D p p p p k n o n p − = − = − = − = − = = = = = − − x y x y x y a K R a y D D D p p p k n o n p 10 ) 2 ( 1 20 ) 2 ( ! 1 20 2 , 1 , 20 , 20 ) 2 .( 4 1 2 3 − = − = − = − = = = = = − + − Seatwork: Find the particular solution of the differential equation. 1. (D 2 – 2D + 8) y p = 16 2. (D 3 + D 2 – 2D) y p = 20 Homework: Find the particular solution of the differential equation. 1. (D 2 – 9D - 3) y p = 27 2. (D 4 – 2D 3 - 5D 2 + 6D) y p = 15...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern