2 diffrential equation quiestions

Math 319 Online

Techniques in Ordinary Differential Equations

Fall 2014

Homework problems to be submitted

Print your name in CAPITAL LETTERS on your assignment. Write clearly and legibly. Show all work and steps, and number your pages. Scan your assignment as a single PDF file .

Assignment 9 (due Sunday November 9, 2014 )

Section 7.1: 2, 9a,b, 12a,b

Section 7.2: 14, 23

Problem 1 : Solve the initial value problem

y′′ + y′ = f(t) + δ(t − 2π), y(0) = 0, y′(0) = 1

where f(t) =

{ sin 2t, 0 ≤ t < π; 0, t ≥ π.

Problem 2 : Solve the integral equation

y′(t) = t +

∫ t 0

y(τ) cos(t − τ) dτ, y(0) = 4.