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insomniac.otaku
 one year 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?
insomniac.otaku
 one year 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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Noliec
 one year ago
Best ResponseYou've already chosen the best response.0I realized I'm not qualified to make a proper explanation of a technique.. :d

Noliec
 one year ago
Best ResponseYou've already chosen the best response.0A general thought is to apply the laws of logarithms though.

Noliec
 one year ago
Best ResponseYou've already chosen the best response.0This 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.

insomniac.otaku
 one year ago
Best ResponseYou've already chosen the best response.1Okay, so does the constant part mess up the e^(at) or is it okay

Noliec
 one year ago
Best ResponseYou've already chosen the best response.0I'm not sure I follow what you mean by mess up the e^(at) :D

insomniac.otaku
 one year ago
Best ResponseYou've already chosen the best response.1sorry. 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.

Noliec
 one year ago
Best ResponseYou've already chosen the best response.0I stand by what I said in the first comment; I'm not qualified enough to say something. Hehe.

insomniac.otaku
 one year ago
Best ResponseYou've already chosen the best response.1Thanks. I wouldn't have thought of the log rules thing.
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