Given: y ′ − 2y =a. draw a direction field for the given differential equation. b. based on an inspection of the direction field, describe how solutions behave for large t. c. find the general solution of the given differential equation, and use it to determine how solutions behave as t → [infinity].

2. y'-2y=t2 e2t

3. y'+y=te to the -t+1

4. y'+(1/t)/y=3cos2t, t> 0

5. y'-2y=3e to the t

9. 2y'+y=3t

10. ty'-y=t squared to the -t, t> 0

12. 2y'+y=3t squared

For a read-a-thon, jay and odhràn each started reading a book at the same time and continued reading for several hours. jay's book had 278 pages, and he read 55 pages per hour. odhràn's book had 238 pages, and he read 45 pages per hour. after how many hours did they have the same number of pages left, and how many pages were left?

Gexpressions: practice question 3 of 5 jackson wants to study the popularity of his music video by tracking the number of views the video gets on his website. the expression below represents the total number of views that jackson's video receives n days after he begins tracking the nu views, where b is the rate at which the number of views changes. alb)" select the statement that would accurately describe the effect of tripling a, the initial number of views before jackson beginst the rate at which the number of views changes, b, will triple. the total number of views the video has after n days, a(b)", will not change. the total number of days since jackson begins tracking views, n, will be reduced by one-third. the total number of views the video has after n days, alb)", will triple. submit

Use the ratio test to determine whether ∑n=14∞n+2n! converges or diverges. (a) find the ratio of successive terms. write your answer as a fully simplified fraction. for n≥14, limn→∞∣∣∣an+1an∣∣∣=limn→∞.