Differential Equations Exam 3

Study Guide For Differential Equations

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) ????(") − 12????$$$ + 53????$$ − 100????$ + 68???? = 500????%&

b) ????’????$$$ − 7????%????$$ + 24????????$ − 34???? = 50????%, ???? > 0

c) 8????$$$ − 12????$$ + 6????$ − ???? = 960????&⁄%

d) ????%????$$ = ????′(3???? − 2????$)

e) 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:

2????’ − 4????)&????$ − ????$$ = ????% sin ???? , ????(0) = −3, ????$(0) = 1