2065f09ex1

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

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

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