2065f09ex1

# 2065f09ex1 - Name: Exam 1 Instructions. Answer each of the...

This preview shows pages 1–2. Sign up to view the full content.

Name: Exam 1 Instructions. Answer each of the questions on your own paper. Be sure to show your work so that partial credit can be adequately assessed. Credit will not be given for answers (even correct ones) without supporting work. Put your name on each page of your paper. A table of Laplace transforms and a short table of integrals are appended to the exam. 1. [16 Points] Solve the initial value problem: y 0 = p ty , y (1) = 4. 2. [16 Points] Find the general solution of: y 0 ¡ (2 =t ) y = t 2 cos t 3. [16 Points] Solve the initial value problem: y 0 + 5 y = y 2 , y (0) = 1 4. [16 Points] Find the general solution of: ( t 3 + y=t ) + ( y 2 + ln t ) y 0 = 0. 5. [5 Points] Complete the following deﬂnition: Suppose f ( t ) is a continuous function deﬂned for all t 0. The Laplace transform of f is the function F ( s ) deﬂned as follows: F ( s ) = Lf f ( t ) g ( s ) = for all s su–ciently large. 6. [15 Points] Compute the Laplace transform of each of the following functions. You may use the attached tables, but be sure to identify which formulas you are using by citing the number(s) in the table, or the name of the principle used.

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.

## 2065f09ex1 - Name: Exam 1 Instructions. Answer each of the...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online