MATH 310 Study Guide - Midterm Guide: Webct, Graphing Calculator, Wronskian

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grayoyster956

1 Dec 2011

School

Simon Fraser University

Department

Mathematics

Course

MATH 310

Professor

Sj Ruuth

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Document Summary

Material: chapters 1,2 and 3 of the text, except sections 2. 8 and 3. 8. Formula sheet policy: you are allowed a cheat sheet on the midterm. You are allowed to modify 1 side of a standard letter-sized piece of paper. It cannot have any wireless capability, or capability to solve di erential equations. Practice: some old midterms were placed on webct. Theorems: (numbers in parentheses give page numbers in 9th edition. : existence & uniqueness: 2. 6. 1 (95-96: method of variation of parameters: 3. 6. 1 (188: wronskians, fundamental sets of solutions, general solutions to homoge- neous and nonhomogeneous equations:

Related Questions

This is from "Elementary Differential Equations" by William E.Boyce and Richard C. DiPrima. It is in chapter 2, section 4. It isproblem number 22.

22. (a) Verify that both y₁(t) = 1-t andy₂(t) = -t²/4 are solutions of the initialvalue problem

yÂ´ = (-t + (t² + 4y)^1/2) / 2, y(2) = -1.

Where are these solutions valid?

(b) Explain why the existence of two solutions of the givenproblem does not contradict the uniqueness part of Theorem2.4.2.

(c) Show that y = ct + c², where c is an arbitraryconstant, satisfies the differential equation in part (a) for t> or equal to -2c. If c = -1, the initial condition is alsosatisfied, and the solution y = y₁(t) is obtained. Showthat there is no choice of c that gives the second solution y =y₂(t).