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Solve the initial value problemry' + (1 + xcot(z))y = 0 with initial condition= 2y(r_...

Question

Solve the initial value problemry' + (1 + xcot(z))y = 0 with initial condition= 2y(r_

Solve the initial value problem ry' + (1 + xcot(z))y = 0 with initial condition = 2 y(r_



Answers

Solve the initial-value problem. $$y^{\prime}+y=e^{2 t}, y(0)=-1$$

Hello to our today. We're going this or problem under 48 here in this it is given that Why? Don't realize, bless Do what it does. Plus why it was Do you know about off my honesty? I never give up. Why have the records to and right? I saw zero. He goes one. I'll play that first time so more Both sides We get what number less is Yes square my office minus s While zero my enough Viad, I shall fiddle Bless you It'll that place rents on My nice is yes Royal Fifth My enough dry off fiddle. A lot less time for values. Why off s Justin cargo ruled by a double My elastic and purpose. I was espresso bar. See? Do any by your first term says Yes, it's quick plus do with plus one Then minus s Y 00 country dress minus four. Why would I shall see rise minus learn. Why are their eyes to our this plus four Richissin Cardo, go by s Pressler. Taking already is to the right. I'm side we get Why Office Indo this still 100 on us? Yes, plus one day or square, which is in cargo so as a square plus Sinus plus seven delivered by Yes, I saw my office. Do you think Arto through a square plus Sorry enough. Plus seven. Do you read it? But yes. Plus Runda who killed reducing cargo? This can be done before and by yes plus one blood be by, especially on the whole square. Seen by as plus, Runde who killed so we can find. See? I think because who was a square plus Sarah, Enough best seven that stood s because minus one they got Yes. Oh, to find a on B. We have to solve by, you know, as president the whole square, plus being Yes, bless one both See because oh, as the square plus sorry enough. Plus seven combat inquisitions off PS square we can find. Here it is. Yeah, it goes. So there is no provision for B and C in a square. Similarly, yes, we can find Go away. Thus be there's no pollution office foresee, which is called a right answer. This seven be because seven miners do it, which is a courtroom three Oh, my office And we don't us. Yeah, but it's not. That is true. by yes press for plus B by a special qualities Do you buy s plus one square. But I see by a specimen whole keep that is ruled by as president He who killed I'm playing inverse LaPlace, Transall or both sides Vivid Buy off the It is a photo to handle about off my nasty plus three d you know, about off my ass t breath in the run by true factor in the square into the bar off my lefty It's can dripping us It is about off. Write a story and go So dress three d bless the square. This can be sold us these choir plus three date plus two. Which is it gonna go the square dress a day? Plus they just to It's gonna unless the Duke Hey, presto! Thus learning new They plus two. So by off day in good into the butt off dynasty into the Bressler and deeper still the accident A fun question. Thank you

Hello for today. You're going to for problem number 27. It is any mission. Ready? Problem? It is given us while you guys bless Cool. Because do you were not a day by zero equals Learn that a player best starts for are both sex via Cape. Yes, my office. My enough, my fellow Plus through my office Because so loveless stands up off. You're enough. They if he did, about minuses. But yes, minuses. But yes. So you get campaigning by office. Yes. Press two by room, people apart. Minus by Yes, well, first get return us to Peter about my process, but yes, you know yes. Plus two plus Barnes doing it, but yes. Plus two. And for Lord by hereby yes, press B, but yes. Plus two. The stupid as secret Tobias to big U equals goodbye after because they couldn't see, uh, cereal? No, but zero plus two. Very physical to a single minus two of you. Good B ecause No, by my restroom, which is because so it'll become in the format. You could apart my SS, dear, but yes, my nest. You did a par minus s there, but yes, Let's do bless barn during but IHS plus two you don't want right? And that's why it is. You are off a bit by enough. You know what? Minus that way, especially it is to find us to be because of they're playing second shipping theater B minus one into your Nothstein? Yes, is do my duty. That's dead. Now for the question. Thank you.

All right. So, first let's start off by determining whether it's an exact differential equation or not. And the way we're going to do that, we're gonna take partial why of each of the X plus why? And partial X. Of two plus X plus Y. E. To the Y. All right. So in the numerator are sorry, on the top partial we'll have Just one and the bottom will also have one. All right. So these two values equal to another. So, we're allowed to conclude that we do have an exact differential equation. So, with this information we can go ahead and carry on with the way we'd like to solve it. So, we'll take the integral of each of the exports why? I'll be integrating with respect to X. And we'll also take the integral of two plus X plus why I E T Y. And will integrate with respect to Y. All right. So the top integral When we integrate you the X we get you to the X. And we integrate why we get X. Y. And then the bottom we're going to get two Y plus X. Y. Plus. Let's see. We should get why E to the y minus E. To the Y. Okay. And so let's go ahead and build our solution by collecting all our like terms. So we have those two matching up and pretty much that's about it. So let's go ahead and write our at our solution will have X. Y plus either the X Plus two. I plus why eating AY minus for you there? Y. Okay. And this all equals to some constant C. And so now that we're given some Initial conditions of Y. of zero Equalling one, we can actually go ahead and solve for this constancy. Okay so the way we're going to do that is we're gonna plug in zero for X. And one for Y. So we'll have E to the zero power, which is one yeah Plus two times 1, which is to plus E minus E equals to see. And so this two cancels out. So we'll have three equals to see. So with that we can build our final answer so X, Y plus E to the X plus two Y plus why? Edith ey minus E to the Y. All equals 23 And that's our answer.

Hello. So the question is taken from the first totally near differential equation where we need to solve this differential equation and the question is L. D. R over duty plus are into I. Is equal to A. And the initial value is the value of current act is according zio is equal to zero. So once again I subscribe disease so they could do okay okay L. E. Ideal. I'll just go and stand okay so let us solve it divide the whole equation by L. So we get the eye over treaty plus are by Ellen to I. Is equal to E by so how we can solve it we can solve it by value in the integrated factor. So integrated factor will be equal to exponential integration our valentine's day. So that will be important to the power our overall entity multiply the whole equation by this integrated victim. We get into the farmers all over hell entity D. I over duties plus. Oh well to the power our entities and I get is equal to you will. Mhm. B To the power our identity. Okay so left hand side of this equation. Can will it on us. The over data. T. To the power our identity and then I. Is equal to or was else B. To the power of L. Entity. Let us take duty to the right hand side of the end integrating so that will be integrating day off into the power of L. Entity and I that is the integration of one that is equal to E over integration into the power to T T. T. Plus you see is the constraint of integration. So left hand side is like integration of one with respect to this quantity. We get into the power alley entity and then I. That is a call you over L. E. To the power our identity and multiply alibi. So I will begins allowed plus since the constraint of education. So let us dividing the whole question by E. To the power viol entity. So I will be equal to if I. R. Plus C. U. To the power minus R. L. Entity. And the boundary condition is that A. T. is equal to zero. Yeah I used to go to. I do. Okay so let us substitute the value of the musical to you. So that will be icu minus E. By art is equal to see. So from here I will be equal to if we substitute the value see E. By our plus I 0 -7. Bye. Uh need to develop minus are by aliens which is required solution of vibration. Hope this clears your doubt and thank you


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