{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

3.5 Method of Undetermined Coefficients

3.5 Method of Undetermined Coefficients - GE 207K Summary...

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

View Full Document Right Arrow Icon
GE 207K Method of Undetermined Coefficients October 3, 2011 Summary: We are dealing with 2nd-order linear nonhomogeneous ordinary differential equations with constant coefficients which can be written as y 00 + ay 0 + by = f ( t ) , (1) where a and b are two CONSTANTS , and f ( t ) is either a sine, cosine, exponential, or polynomial (or a constant). In this method, we will wisely choose a form for the particular solution which will have some unknown coefficients. Later solve for these coefficients. Steps : 1. Find the corresponding homogenous solution, y h : Set the f ( t ) equal to zero, and find the corrensponding solution to the differential equation. In other words, solve the differential equation y 00 + ay 0 + by = 0 (2) and call the solution y h . 2. Find the particular solution, y p : (i) For a given f ( t ) , choose a form for y p from table below: f ( t ) y p Ke γt Ae γt K cos ωt A cos ωt + B sin ωt K sin ωt Ke αt cos ωt e αt ( A cos ωt + B sin ωt ) Ke αt sin ωt Kt 4 At 4 + Bt 3 + Ct 2 + Dt + E 1 , 5 , 10 , 31 , 59 , etc. A Kt 3 e γt ( At 3 + Bt 2 + Ct + D ) e γt (ii) Modification rule – If the form chosen for y p appears in y h , multiply your choice for y p by t , and recheck . (See Example 2 for an example of this). Keep multiplying y p by t
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
Image of page 2
This is the end of the preview. Sign up to access the rest of the 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