{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

pmidterm1

# pmidterm1 - 3(a(10 points Show that the following equation...

This preview shows pages 1–8. Sign up to view the full content.

Math 33b Midterm 1 Lecture 2 Fall 2007 Name: Section: Instructions: There are 6 problems. Make sure you are not missing any pages. Show all work in detail or your answer will not receive credit. Write neatly and box all answers. No calculators, books, or notes are allowed. Answer the questions in the spaces provided on the question sheets. If you run out of room for an answer, continue on the back of the page. Do not use your own scratch paper. Extra scratch paper is available from the front of the room. Question Points Score 1 20 2 20 3 20 4 20 5 10 6 10 Total: 100

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

View Full Document
1. (20 points) Solve the initial value problem: t dy dt + (2 t 2 + 3 t 3 ) y = te - ( t 2 + t 3 ) , y (0) = 5
2. (a) (10 points) Solve the initial value problem: dy dt = 2 t ( y - 1) 2 , y (0) = 0 (b) (10 points) Solve the initial value problem: dy dt = 2 t ( y - 1) 2 , y (0) = 1

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

View Full Document

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

View Full Document

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: 3. (a) (10 points) Show that the following equation is exact: 2 x + y 2 + 2 xy dy dx = 0 (b) (10 points) Find the explicit solution to the initial value problem: 2 x + y 2 + 2 xy dy dx = 0 , y (1) = 1 4. (20 points) Find an integrating factor for the following equation (you do not need to solve the equation): 4 x 2 y + 2 y 2 + (3 x 3 + 4 xy ) dy dx = 0 Hint: It is of the form μ ( x, y ) = xy a for some a . 5. (10 points) Solve the initial value problem: dy dx = sin( πy )(2 y-4)( y 3-6 y 2 + 12 y-8) , y (1) = 2 6. (10 points) Find the equilibrium solutions for the following equation, and identify them as asymptotically stable or unstable. dy dt = y 2-5 y + 6 Extra Scratch Paper:...
View Full Document

{[ snackBarMessage ]}

### Page1 / 8

pmidterm1 - 3(a(10 points Show that the following equation...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online