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Tvdoo onnito Onpnsncstvsn Ac 0oc 4 SoccY{ 3t...

Question

Tvdoo onnito Onpnsncstvsn Ac 0oc 4 SoccY{ 3t

Tvdoo onnito Onpnsncstvsn Ac 0oc 4 SoccY{ 3t



Answers

$$\mathscr{L}\left\{t^{3}-t e^{t}+e^{4 t} \cos t\right\}$$

Okay. Good day. Ladies and gentlemen, today we're looking at problem number 11 here. And the question is whether or not we can apply the domesticated of undetermined coefficients Thio this, uh, ordinary different show equation here. And so I'm not really gonna, um, go through all the different parts of the undetermined coefficients cause I think there's probably 5 to 6 distinct cases. But it is important, I think, for you two know each of those cases because they tell you how to go about solving, um, the, uh, ordinary differential equations. They'll tell you how to solve a bunch of cases of, or a bunch of, um, ordinary difference, your equations on particular ones with constant coefficients here. And so the first thing is to realize that, um oops, sorry about that. So if I take three different, distinct functions, I think one of the year of two of two here at three of tea Now I'm going to really look at this case by case in each case. So in the first case, this one here is, um and it is in fact, a proper form. It is one of the cases, and I'm not sure which But if you look, if you flip through, you'll see the thing cases. And this is in fact, one of the cases, um, in the 2nd 1 here again is also a case again. I don't know exactly what's important, but it is, in fact, one of the cases covered by the, um, undetermined coefficients. But the 3rd 1 is not and in particular one over tea is not a polynomial. It is Tito the negative first, and that is not, um, covered by any of the cases. So in particular than, um, since you have one I mean, really, you can't get rid of this one over t s o. The end of the final answer is that it's not applicable, and it's not applicable because there's no case that covers us. And the older way you could solve this. Using the undetermined coefficients is to break this into threes. In cases here, I'm solve each one and then applies the the superposition principle. And in this case, you can't because one of those, uh, you know, is not solvable using that method. Uh huh. But it doesn't mean that there's not other methods to solve it. It's just not solvable using this method really, all the collections after. So there's no need to go any further with. So, um, again, I would just mention that, um, it's a good idea to have in the back your mind. What thes, um the what the undetermined coefficients method involves and sort of go through each of the steps because it's it's actually fairly involved. There's quite a few different steps, and there's a bunch of different cases. So there kind of TVs, but still probably could know. Uh, okay, so that's it for this problem. Thank you very much. I haven't.

In this problem let us first look. And the left hand side of the equation Which is on one or two R three. This becomes delta upon s minus C. Into delta upon s minus B. Into delta upon s minus C. This becomes data cube upon as minus C. As minus B. S minus C. Multiplying and dividing my S. This becomes as delta cube divided by sister the square. This is delta times. Yes. Now let us look at the right hand side of the equation. Use the fact that caught off A by two, there's nothing but under root. S S minus A upon yes minus B into s minus C. Similarly carter B by two. Yes as s minus B upon S minus E. S minus C. And caught off see back to as as S minus C upon s minus A. And to s minus B. So from here the right hand side of the equation becomes this is our cube. And do my application. Oh Court Square. A court squared B by 20 courts by sea by too well give us mrs S s minus A upon s minus B as minus C. Into us as minus B upon s minus E into s minus C into us S minus C. Born s minus E into the s minus B. As fantasy. As fine as being s minus C. Each get cancelled we are left with rQ into s cube divided by s minus E. S minus B as minus C. Multiplying this by S this bias are into ss delta. So this is delta cube into a divided by this is delta square, which comes as delta into us. And we see that Alleges is equals two our ages hence.

In this video is gonna go through the solution to question 36 in chapter 4.5 so as to find the correct form of a particular solution to this differential equation. So first we look at the genius part, it would be easier if we write this like t squared minus one or multiplied by Thio. Either to t we're gonna stake out to tea is a factor. So now we see that, and but that we have a exponential term was by by phoning better. So this motivation is execute her solution off the form a zero plus a one. See this A to t squared. It's That's a general polynomial border, too. Ties by eats the two tea because that's what we have in the Virginia, sir. But before we're confident that that's gonna work, we need to check the auxiliary equation in this case is R squared minus for our plus four is equal to zero. That's the same as, uh, minus two squared is equal to savor, so that, uh, is equal to to a double room. Said this is problematic because we have a room of the axillary equation this equal to the degree of the polynomial in the in her Virginia's term. So therefore, to modify this particular at this form of that particular solution when you multiply it by t square, the two you could involved the solution here. So now this will give us this gives us the appropriate form off secret in particular solution to this.

Question is this compound is given in this compound. Here is hydrogen. Here is the history. Here is a education, including it is like. So we can observe that this hydrogen in this prison. Both are present at the anti position. That's why this component, the anti trans. For john's why 1234 trance, one kg four mid time cyclo hexane. We give number one to the chlorine carbon because chlorine comes first in the english alphabet. During means. See see comes first in the english alphabet. Dana M. In the metal group. That's what great options we see.


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