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EEGR.505 Advanced Analytical and Computational Engineering Mathematics
Homework 3
Due Date: Monday, October 27, 2003
Problem 1
Consider the the system of ordinary differential equations given by
(∂x(t)
∂t + 2 ∂y(t)
∂t −2y(t) = t
x(t) + ∂y(t)
∂t −y(t)=1
with the initial condition x(0) = 0 and y(0) = −2.
1. Write down the system of equations.
2. Compute its Laplace transform.
3. Solve the new system in the Laplace transform space.
4. Compute the inverse Laplace transform to obtain the solution (x(t), y(t)).
5. Plot the solution (x(t), y(t)) for t∈[0,1] (hint: parametric plot).
Problem 2
Consider the integral equation
f(t) = 1 + Zt
0
sin(t−u)f(u)du.
Find the function f(t) (show all your steps).