### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Class Note for MATH 250A with Professor Lega at UA

### View Full Document

## 17

## 0

## Popular in Course

## Popular in Department

This 5 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 17 views.

## Popular in Subject

## Reviews for Class Note for MATH 250A with Professor Lega at UA

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 02/06/15

Calculus and Differential Equations ll MATH 250 B Other types of linear equations Cauchy Euler equations a Cauchy Euler equations are of the form ant y l an1t 1y 1 l l alty l aoy ft7 where the coefficients a are given constants o The change of variable t equot if t gt O and t iequot if t lt O transforms a Cauchy Euler equation into an equation with constant coefficients for y as a function of X The resulting equation may then be solved as usual 0 Of course the general solution yx must be re written in terms of t at the end of the calculation dzy dy dtz l HE l 25y cos 4 lnt l lnt 9 Example Solve t 2 for t gt 0 Higher order equations with constant coefficients 9 The methods discussed previously may easily be generalized o The characteristic equation associated with anyquot an71y 1 311 301 flx is a polynomial of order n with real coefficients 9 Because the coefficients are real the roots are either real or complex conjugate pairs 0 A real root A of multiplicity 1 gives a solution 5 O A real root A of multiplicity p gt 1 gives p solutions 5 X5 XZEAX I I I XpileAX 7 7 0 Complex conjugate roots A a i 5 give solutions 50 cos x and so sin x 0 Complex conjugate roots A a i B of multiplicity p gt1 give 2p solutions 50 cos x so sin x X 50 cos x X 50 sin x etc Higher order equations continued 0 The method of variation of parameters and the method of undetermined coefficients can also be extended 9 Example Solve ym 7 5yH12yli 8y e3t cos2t l Her 9 Variation of parameters for instance for a third order linear equation ify1y2 and y3 are three linearly independent solutions to the homogeneous equation we set Yp U1Y1 LIN2 U3Y3 With 0 UlY1U2 2U3Y37 0 uiyiu y u y 7 flxl 7 1Y1 2 2 3Y3 3X The determinant of this system which is the Wronskian of y1 y2 and y3 is non zero since the three solutions are linearly independent Other linear equations For linear equations of order n which do not have constant coefficients and are not Cauchy Euler equations try the following 0 Find by inspection one solution to the homogeneous equation 9 Use the method of reduction of order repeatedly to find n linearly independent solutions to the homogeneous equation 9 Write the general solution to the homogeneous equation yh as a linear combination of the above n linearly independent solutions 9 Find a particular solution yp by inspection by the method of undetermined coefficients or by variation of parameters 9 Write the general solution y yh yp 6 Apply initial or boundary conditions if any

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "I signed up to be an Elite Notetaker with 2 of my sorority sisters this semester. We just posted our notes weekly and were each making over $600 per month. I LOVE StudySoup!"

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.