{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

09FDC9DCd01

# 09FDC9DCd01 - y(0 = 7(a What is the longest interval in...

This preview shows pages 1–5. Sign up to view the full content.

M427K EXAM 2B Your name: SPRING, 2010 Dr. Schurle Your UTEID: Show all your work on these pages. Be organized and neat. Your work should be your own; there should be no talking, reading notes, checking laptops, using cellphones, . . . . 1. (15 points) Find the general solution of y 00 - 3 y 0 + 2 y = 8 t + 20 cos 2 t.

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

View Full Document
YOUR SCORE: /100 2. (15 points) The linear differential operatior L is given by L = ( D - 5) 3 ( D 4 + 16) . Find the general solution of L [ y ] = 0. 3. (15 points) Write the simplest form of a particular solution y p of the following dif- ferential equation. DO NOT EVALUATE THE CONSTANTS that appear in your answer. y 00 - 12 y 0 + 36 y = 7 t 2 e 6 t + 2 t 3 - 4 te - 6 t sin(3 t )
4. (10 points) Consider the following initial value problem. ( x 2 + x - 6)( x - 7) y 00 + 4 xy 0 - 3 y

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: , y (0) = 7 (a) What is the longest interval in which you are sure that a solution exists? (b) Could the power series solution centered at x = 0 be used to get a good approx-imation for y (1 . 5)? Why or why not? 5. (15 points) Find the general solution of ( x-7) 2 y 00-5( x-7) y + 13 y = 0 on x < 7. 6. (15 points) Find the general solution of x 2 y 00-3 xy + 4 y = 2 x 2 ln x on x > 0. 7. (15 points) Find the recurrence relation and the ﬁrst four nonzero terms of the power series solution centered at x = 0 for the initial value problem (1-x ) y 00 + 2 xy + 3 y = 0 , y (0) = 6 , y (0) = 1 ....
View Full Document

{[ snackBarMessage ]}