﻿ Study guide for differential equations - Essay solutions

## Study guide for differential equations

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Study Guide for Exam 3

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Show absolutely all work. Start each problem on a new page. Label them clearly.

The Problems
1. Find the general solutions of the given differential equations, initial value problem, and

system using whichever method that seems appropriate.

a) (4) 12 + 53 100 + 68 = 5002x

b) 3 72 + 24 34 = 502, > 0

c) 8 12 + 6 = 960×2

d) 2 = (3 2)

e) 4()2 = ()4 + 3, assume x is the independent variable.

f) 2 + 2 + = + 1, + 3 + + = 4 + 14. (Eliminate x first!)

2. Find the first six non-zero terms of a Taylor series solution to the initial value problem:

23 4-x = 2 sin , (0) = 3, (0) = 1 Name:

Study Guide for Exam 3

Show absolutely all work. Start each problem on a new page. Label them clearly.

The Problems
1. Find the general solutions of the given differential equations, initial value problem, and system using whichever method that seems appropriate.

a) (4) 12 + 53 100 + 68 = 5002x

b) 3 72 + 24 34 = 502, > 0

c) 8 12 + 6 = 960×2

d) 2 = (3 2)

e) 4()2 = ()4 + 3, assume x is the independent variable.

f) 2 + 2 + = + 1, + 3 + + = 4 + 14. (Eliminate x first!)

2. Find the first six non-zero terms of a Taylor series solution to the initial value problem:

23 4-x = 2 sin , (0) = 3, (0) = 1

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