{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Quiz5 - C 2 cos x e x 2 Verify that this is indeed the...

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

MATH 2930 Summer 2009 Quiz 5 NAME: Cornell NetID: 1. Solve the following eigenvalue problem and report all the eigenvalues and all corresponding eigenfunctions. y + λy = 0; y (0) = y (2 π ) , y (0) = y (2 π ) . (1)

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

View Full Document
2. Solve the following differential equation by using the method of power series. y + y = e x . (2) Note that by using the techniques learned earlier in the course you can solve the equation to get the solution as y ( x ) = C 1 sin(
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ) + C 2 cos( x ) + e x / 2. Verify that this is indeed the solution to the given problem. Now try to match your power series solution to given solution. Does it match? If not, then how do you explain the apparent paradox? You may use the following: sin( x ) = x-x 3 / 3! + x 5 / 5!-. . . , cos( x ) = 1-x 2 / 2! + x 4 / 4!-. . . , e x = 1 + x + x 2 + . . . . 2...
View Full Document

• Spring '07
• TERRELL,R
• Math, Eigenvalue, eigenvector and eigenspace, Classless Inter-Domain Routing, Eigenfunction, following differential equation, power series solution, following eigenvalue problem

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern