{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

202y05mt1 - B U Department of Mathematics Math 202...

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

View Full Document Right Arrow Icon
B U Department of Mathematics Math 202 Differential Equations Summer 2005 First Midterm This archive is a property of Bo˘ gazi¸ ci University Mathematics Department. The purpose of this archive is to organise and centralise the distribution of the exam questions and their solutions. This archive is a non-profit service and it must remain so. Do not let anyone sell and do not buy this archive, or any portion of it. Reproduction or distribution of this archive, or any portion of it, without non-profit purpose may result in severe civil and criminal penalties. 1. Using Abel’s Theorem and the fact that y 1 = 1 t + 1 is a particular solution of the differential equation, solve the initial value problem: ( t 2 - 1) y + 4 ty + 2 y = 0, y (0) = - 5, y (0) = 1. What is the interval of validity? Solution: y 1 y 2 - y 2 y 1 = ce - R p ( t ) dt , p ( t ) = 4 t t 2 - 1 choose c = 1 1 t + 1 y 2 + 1 ( t + 1) 2 y 2 = 1 ( t 2 - 1) 2 ( t + 1) y 2 + y 2 = ( t + 1) 2 ( t 2 - 1) 2 (( t + 1) y 2 ) = 1 ( t - 1) 2 ( t + 1) y 2 = - 1 t - 1 + k, k R y 2 = 1 t - 1 [or, equivalently, y 2 = 1 t 2 - 1 ] Hence the general solution is
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