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insomniac.otaku

  • 2 years ago

I apologize if my question is not super specific. I just watched lecture 13 which is on finding particular solutions to inhomogeneous equations. In the video he mentions functions of importance, which were e^ax, sin(wx), cos(wx), e^(ax)sin(wx), e^(ax)(cos(wx)). In all of these cases, as far as I understand, he rewrote them in the form e^(a+iw). I did not in the lecture see any cases where you have something like t*e^t+4. I am not sure how I would get it in that e to the whatever form or even if it is possible. Is the technique even valid in that case?

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  1. Noliec
    • 2 years ago
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    I realized I'm not qualified to make a proper explanation of a technique.. :d

  2. Noliec
    • 2 years ago
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    A general thought is to apply the laws of logarithms though.

  3. Noliec
    • 2 years ago
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    e^(ln(t))*e^(t)+4

  4. Noliec
    • 2 years ago
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    This means that t>0 though; so it might falsify the solutions in the end. If you're supposed to use imaginary stuff I got no clue as to how they apply in combination with exponential functions and their inverses.

  5. insomniac.otaku
    • 2 years ago
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    Okay, so does the constant part mess up the e^(at) or is it okay

  6. Noliec
    • 2 years ago
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    I'm not sure I follow what you mean by mess up the e^(at) :D

  7. insomniac.otaku
    • 2 years ago
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    sorry. In the lecture he said that you can rewrite your f(x) as e^((a+iw)x). When I mentioned a I meant the complex factor and the 't' was the x. So I was wondering if the f(x) portion was okay being something like e^(a+iw)x + g, where g is a constant.

  8. Noliec
    • 2 years ago
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    I stand by what I said in the first comment; I'm not qualified enough to say something. Hehe.

  9. insomniac.otaku
    • 2 years ago
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    Thanks. I wouldn't have thought of the log rules thing.

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