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You are not logged in. #26 20131212 09:21:09
Re: Wronskian use identities !That makes v1(x) = v2(x) which makes the determinant 0 that means they are linearly dependent. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #28 20131212 09:24:41
Re: Wronskian use identities !Hi evinde The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #29 20131212 09:25:52
Re: Wronskian use identities !Why is the Wronskian non  zero? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #30 20131212 09:26:41
Re: Wronskian use identities !Because the exponential function is always nonzero. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #31 20131212 09:28:27
Re: Wronskian use identities !The determinant is 0 because v1(x) = v2(x), therefore the Wronskian is 0. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #33 20131212 09:29:37
Re: Wronskian use identities !Isn't that what are you trying to prove? Using it in the proof would be circular reasoning?! In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #35 20131212 09:32:01
Re: Wronskian use identities !Find the determinant of the system of equations given in the second to last line of your post 1. You will see that it actually represents the Wronskian at x=0. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #36 20131212 09:37:32
Re: Wronskian use identities !
Don't you mean these two: , d_{1}{v_{1}}'(0)+d_{2}{v_{2}}'(0)={f}'(0) ?Can I find the determinant,although I haven't shown that there and that satisfy these conditions?? Last edited by evinda (20131212 09:41:16) #37 20131212 09:40:43
Re: Wronskian use identities !Well, the point of finding the determinant is to show that there are solutions, so, yes, you can. Of course, you should treat d1 and d2 as the unknowns when finding the determinant. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #38 20131212 09:43:29
Re: Wronskian use identities !
So,I find the determinant and notice that it equals to the Wronskian,so it is .And then?#39 20131212 09:50:29
Re: Wronskian use identities !Yes, but first you need to find the Wronskian. You can do this using Abel's identity. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #42 20131213 00:39:40
Re: Wronskian use identities !What did you get for In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #44 20131213 00:49:14
Re: Wronskian use identities !What do you get for v1(x) and v2(x)? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #46 20131213 01:06:41
Re: Wronskian use identities !It has been stated the v1 and v2 are the 2 solutions to the DE. Do you agree? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #47 20131213 03:33:18
Re: Wronskian use identities !There is an infinite nunber of solutions of the DE. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #48 20131213 05:24:52
Re: Wronskian use identities !Without fixing c1 and c2, that determinant will always be zero. That means the Wronskian will be 0. Do you agree? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #49 20131213 05:26:54
Re: Wronskian use identities !Huh? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #50 20131213 05:28:36
Re: Wronskian use identities !(v1(0)v2'(0)v2(0)v1'(0)) In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 