{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Homework-6-s12-SOLUTION

# Homework-6-s12-SOLUTION - 1 AMS 361 Applied Calculus IV by...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 AMS 361: Applied Calculus IV by Prof Y. Deng Homework 6 Assignment Date: Wednesday (02/29/2012) Collection Date: Wednesday (03/21/2012) Grade: Each problem is worth 10 points. Problem 6.1 Find the general solution of the following equation ࠵ − 3 ! ࠵ − 2 ! ࠵ ! − ࠵ + 2 ࠵ ( ࠵ ) = where ࠵ ≡ ࠵ ࠵¡ Solution: From the DE, general solution is given by sum of general solutions of the three DE’s ࠵ − 3 ! ࠵ = ࠵ − 2 ! ࠵ = ࠵ ! − ࠵ + 2 ࠵ = For ࠵ − 3 ! ࠵ = , solution is ࠵ = ࠵ ! + ࠵ ! ࠵ ࠵ ! ! For ࠵ − 2 ! ࠵ = , solution is ࠵ = ࠵ ! + ࠵ ! ࠵ + ࠵ ! ࠵ ! ࠵ ! ! For ࠵ ! − ࠵ + 2 ࠵ = , solution is ࠵ = ࠵ ! ࠵ ! ! + ࠵ ! ࠵ ! ! , where ࠵ ! , ࠵ ! are zeros of the characteristic polynomial ࠵ ! − ࠵ + 2 = ⇒ ࠵ ! , ! = ! ! ± ! ! ! If we like to express the solution in real-value (at least it appears), it can be rewritten as ࠵ = ࠵ ! ! ࠵ ! sin ! ! ࠵ + ࠵ ! cos ! ! ࠵ The general solution to the original DE is then ࠵ = ࠵ ! + ࠵ ! ࠵ ࠵ ! ! + ࠵ ! + ࠵ ! ࠵ + ࠵ ! ࠵ ! ࠵ ! ! + ࠵ ! ! ࠵ ! sin 7 2 ࠵ + ࠵ ! cos 7 2 ࠵ . Problem 6.2 Find the general solution of the following equation ࠵ ࠵ ࠵¡ − ࠵ ! ࠵ ࠵ = where ࠵ = constant and ࠵ = positive integer 2 Solution: The solution to ࠵ ! !" − ࠵ ࠵ ! = has multiplicity ࠵ , so the general solution will contain terms similar but linearly independent from the first order equation....
View Full Document

{[ snackBarMessage ]}

### Page1 / 5

Homework-6-s12-SOLUTION - 1 AMS 361 Applied Calculus IV by...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online