代做Mathematics 376: Ordinary Differential Equations Assignment 3帮做R编程

Mathematics 376: Ordinary Differential Equations

Assignment 3

Note: This assignment consists of 5 problems of equal weight.

Due: After Unit 11

1. Find Laplace transforms for the following function

2. Find the partial fraction expansion for:

and, on this basis, find the inverse Laplace transform, L−1 {P}.

3. Find

using the convolution theorem.

4. Solve the following initial value problem

5. Given one initial condition y(0) = 0, find a value of parameter a such that the solution of the IVP

satisfies the condition y (2/π)= 1.