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Solve the initial value problem: v" 6y + 14y = 0, 9(o) = 4 4(0) = 1.Give your answer AS yUse € aS the independent variable.Answer:...

Question

Solve the initial value problem: v" 6y + 14y = 0, 9(o) = 4 4(0) = 1.Give your answer AS yUse € aS the independent variable.Answer:

Solve the initial value problem: v" 6y + 14y = 0, 9(o) = 4 4(0) = 1. Give your answer AS y Use € aS the independent variable. Answer:



Answers

Solve the initial-value problem.

$ 4y" - 20y' + 25y = 0 $,


$ y(0) = 2 $,


$ y'(0) = -3 $

Here we have to solve the initial value problem, which is given by nine y double prime last fourth white brain plus four way since he called to see you and the initial value, sir, Why zero is equal to one on white crime. Zero? Yes, he called to zero. So now we can associate the characteristic excavation. Tow this differential equation which kind of glutinous? 90 square plus 12 t plus four is equal to zero. So this is nothing but three t plus two. Whole square is equal to zero. So this imply it steams the call to negative to over three. Now we see that there is only one route in the captured stick excavation. So then the fundamental solutions to this differential commissions are going to be to depart negative tooth hurt X comma. It's times e to the poor. Negative to third ex to these are the two fundamental solutions. No, it's internal solutions. It's going to be Why is he called to see one times e to the bar. Negative to third ex plus C two times x times e to the power Negative 2 36 which can be also return us. You to the port. Negative tooth hurt X time, See? One plus C two weeks. So now our goal is to determine this C one and C two. So now there. See? We have Why zero is a call to one. This in place C one plus C two times zero Is he going to one? So the same place he want is going to one. We have found our Steve one. So let's take the derivative. Why Prime X? It's going to be e to the power negative to third X by the product rule. And then I have been negative. Tooth hurt time see one plus C two weeks plus you to deport Negative to third ex. I don't see too No, I have Why Prime zero is equal to zero. See if I take white prime zero, I end up getting negative to third time. See? One plus fee to is he called zero. So now I already found our C one is equal to one. So I have C two. Is he called to positive tooth hurt. So no lives right down the final solutions which can return us. Why is he going to eat to the bower. Negative two x over three time see one, which is one plus e to which is to over three times six. So that is a large bird. Equal a solution. Tow this initials a new problem.

Hello. Even in this human question, we have to solve the initial value problem. The question is for the white devilish plus for my dash plus three wise equals to Jesus, right? An initial conditions which are given us. Why you guys equals judo and why Distrigas equals to one like so fast. We had to find oxalate immigration. We have to find the votes off the exhilaration. Then, according to this, we will find the general form off the solution. So can we get the auxiliary creationists? Four plus crazy questo zero. Right. So we get the roots off this equation says, um, are Sequels to minus four plus minus. Followed Toyota divided by eight, which is a class minus one by two plus minus one by two her I oughta lied under Toyota like, uh, so since the roots are imaginary roots, so we have the general form off. The solution is ive to depart minus one. Bite works. See one because one by two under two works plus see to sign fun by 202 works, right? This is the final form of the solution. Now we'll find the Y dish by dish is equal to minus one by two A double minus one by two weeks. Stephen costs one by 22 weeks plus C to sign one by two good works plus eight to the bar minus one Might works minus even sign one by 22 weeks plus sito Because one by two, two x and the common will come that this, uh So here common will come That is one by two in tow with the help off. 10 differentiation. Right? So now we have a different initial conditions. That is why Gina is one. Why didn't say close to zero? So why do you guys? It was 21 into seven cost, you know, plus C to sign zero, which is a quest to see one. So we had a value of C one and C equals to zero. Thank you. Now, the second initial condition. Virus traders. It was one. You just think once the Geo plus one Jacob Placido, cause one by two works, um, multiplied by one by two. Go to is equals to one. Right. So we have the value off. So when you simplify this, we get C two one by two. Is it close to one. So we have the value of C two s under do right, so we can substitute the values off C one and C two in the general. Former solution. We get by access under 28 depart minus X by two. Sign one by two go to X. Right. So this is the final solution for the initial value problem.

Hello, everyone. And the young question we have to find We have to solve the initial value problem that is Read y devilish minus two y dish minus. Why is it close to zero? And the two conditions boundary conditions are given. That is why you guys equals to zero And why the status equals t minus fourth. Hey, so for this question, uh, first, in order to solve the initial value problem, we will first solve, like, even differential equation. The auxiliary question is three rd squared minus two are minus. One is equals to zero. The roots off the situation will be I want to. Will be to plus minus handled. Be square that is minus two squared minus four. Divided, by the way. Right. So this comes out to me. I want to its request toe one and minus one battery. Right. So these are the two lots to roots off The given equation given are slightly equation. So does that self. The general solutions For this all the question will be why exit was toe see one a to the power of an X plus Cito eight to the bar to excite. So it's substitute the value off one and all to we will get, See, Even eat the power X plus C toe to the ball minus X by tree Like so this is the general form. Now we'll substitute now we will first computer derivative off The general solution first will computer very with you So we will get when we differentiated you get seed money to the products plus Ito minus one by three Eat about minus one by three x night So we will get why dish access See Veneto The products minus one by three see to you to depart minus one by three x like no, uh, from the US From the first initial condition we have I Jesus equals to zero So therefore see, even eat the bulges A plus c two e two The bowel Jesus equals Jesus means even plus heat equals to Jesus. I'll see you. Any Sequels to minus here tonight? Now, from the second initial condition, we have Vitus generous minus full like so. Stephen. Eight apologies. Uh, minus one by three Cito eight Apology. The s minus four. Since he when it's equals minus since even is it was a minus. Ito, right So we get, uh, minus 30 to minus C two by three is request to minus four or C two is equals to, uh, t late. So see you in its equals T minus sea to mid minus tree. So these are the values of C one and C two. Now we'll have to do this value so we'll get solution to the initial value. Problem is minus three to depart X plus three to the bubble minus expertly. Right. So this is the final solution for the given initial value.

Hello, everyone. In this given version, we have toe solve the initial value problem. The question is why devilish minus six Swedish plus 10 by it's a question and to initial conditions are given. That is wise. You guys too. And why does judo is three right? So first real light oxidant equation. So you get ice with minus six hour plus tenets Request ejido on the routes off. These equations are six plus minus and the 36 minus 40 divided by toe which comes out Toby six Celtics comes out to be three plus minus iota. So these are the 32 off the Given the question, since the roots are imaginary roots. So we have the general solution that is to the body X See one Cosby X plus C to sign bx tonight. Now, uh, a question. This is given the book so we'll plug the values from the roots that is is request to three and basic was too one like so it took about three x see, even cortex plus C to cynics. Now we have to find the values of C one and C two to find the value of C one and C two, We have toe put initial conditions. So why did you go? Is equal to which is equals to U to the power ejido. See you on cost you plus C to sign Jill. So this will give the u. N. Has to like now we will differentiate it. So when we differentiate the VX, we get virus access I hated about three x minus even cynics plus C two Cossacks plus three to the Power three x See you on Cossacks, Stephen cause t a X. So this even cause three X plus Ito Synnex. Right now we have the second initial value problem. That is why the studio is equal to three. So we get to the college. Edo Um minus even signed judo plus C to cost, you know, plus three to depart Judo C one cause street off Aceto Sandretto Like eso, this will result in, say, two plus 37 We know the value off Stephen. That s e questo. So c two plus, So this will give the result off Saito a spine astri Wright. Now we can put substitute the values off C one and C two in the general form. So we get wires created about three X to Cossacks minus three. Cynics. Right. So the sisters solution for the initial value problem.


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