Homework 5, due February 29, 2008.

[goodwine]

Use Laplace transforms to solve each of the following differential equations.

1. Find the solution to
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2. Find the solution to
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3. Find the solution to
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4. Find the solution to
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5. Find the solution to
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6. Find the solution to
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7. Find the solution to
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8. Find the solution to
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   The function 1(t) is the step function, as discussed in class.
9. Find the solution to
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   Either write your own computer program or use matlab to verify your solution. Submit a plot of the solution you obtained by hand and a plot of the numerical solution. If they are not the same, explain any differences.
10. Find the solution to
    • 
11. Find the solution to
    • 
    Either write your own computer program or use matlab to verify your solution. Submit a plot of the solution you obtained by hand and a plot of the numerical solution. If they are not the same, explain any differences.

[colinheye]

I am guessing that the function is supposed to be 't' from 0 to 1, and not t to 1. Is that correct?

[goodwine]

I am guessing that the function is supposed to be 't' from 0 to 1, and not t to 1. Is that correct?

Yes, that's right. I fixed it.

[goodwine]

For problem 7 on the homework, the delta function has the Laplace
transform to e^(-s*tau), and I'm a little lost as far as how to reverse
transform that in combination with the rest of the equation. If you
could point me in the right direction that'd be great.

Unless I'm misunderstanding the question, what will happen is that it will end up multiplying the stuff that comes from the derivatives on the left hand side of the differential equation. Then you just use the time delay property from the chart.

[kwilson7]

Hi, just wanted to know when/if the solutions to this HW will be posted. Thanks.

[goodwine]

Hi, just wanted to know when/if the solutions to this HW will be posted. Thanks.

I don't know why I hadn't posted them yet. Regardless, they are there now.