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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.

 

1. ?^(“) − 12?^$$$ + 53?^$$ − 100?^$ + 68? = 500?^%&

 
 
 

1. ?^’?^$$$ − 7?^%?^$$ + 24??^$ − 34? = 50?^%, ? > 0

 
 
 

1. 8?^$$$ − 12?^$$ + 6?^$ − ? = 960?^&⁄%

 
 
 

1. ?^%?^$$ = ?′(3? − 2?^$)

 
 
 

1. 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