Written homework #5.

Written homework #5.

Problem #1: Find the general solution of the following system of equations and describe the behavior of the solution

as t ! 1. Plot a few trajectories of this system.

Problem #2: Find the general solution of the following system of equations and describe the behavior of the solution as t ! 1. Plot a few trajectories of this system.

Problem #3: Find the solution of the following initial value problem and describe the behavior of the solution as

Problem #4: Find the general solution of the following system of equations and describe the behavior of the solution as t ! 1. Plot a few trajectories of this system.

Problem #5: Find the Laplace transform of the function f(t) = 4e

Problem #6: Find the inverse Laplace transform of the function F(s) =

5e

Problem #7: Find the inverse Laplace transform of the function F(s) =

Problem #8: Use the Laplace transform to solve the following initial value problem.

Problem #9: Use the Laplace transform to solve the following initial value problem.

Problem #10: Use the Laplace transform to solve the following initial value problem.

Problem #11: Use the Laplace transform to solve the following initial value problem.