20d_04s_2e

20d_04s_2e - 3. (9 points) y = t and y = t 2 are solutions...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 20D Second Midterm 48 points May 26, 2004 Print Name, ID number and Section on your blue book. BOOKS and CALCULATORS are NOT allowed. One side of one page of NOTES is allowed. You must show your work to receive credit. Some integrals and derivatives that may be useful: i tan x dx = - ln(cos x ) + C (tan x ) = sec 2 x (sec x ) = sec x tan x i sec x dx = ln(sec x + tan x ) + C (arctan x ) = 1 1+ x 2 (arcsin x ) = 1 1 x 2 1. (27 points) Find the general solutions of the following di±erential equations. (a) y - (tan x ) y = 1 (b) y ′′ - 2 y + y = 4 t (c) ( x 2 + 1) y - y = 0 . 2. (3 points) I have decided to ²nd a series solution y = a n x n to (4 + x 2 ) y ′′ + (1 - x ) y = 0 . For what values of x can you guarantee that the series will converge? Why? You must give a reason —the “Why?”— to receive credit.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 3. (9 points) y = t and y = t 2 are solutions to t 2 y -2 ty + 2 y = 0. Find a particular solution to t 2 y -2 ty + 2 y = t 2 e t . You may leave integrals in your answer. 4. (9 points) y ( t ) satises the dierential equation y ( t ) + y ( t-1) = 1 , with y ( t ) = 0 for t 0. Compute the Laplace transform Y ( s ) = L{ y ( t ) } . When your exam is returned, it will have the grade you will receive if you do NOT take the nal exam. In computing that grade, this exam will be weighted more than the rst exam to reect the fact that the nal will emphasize dierential equations. END OF EXAM...
View Full Document

This note was uploaded on 06/18/2009 for the course MATH 20D taught by Professor Mohanty during the Fall '06 term at UCSD.

Ask a homework question - tutors are online