5

3. Solve the initial value problem_y" - 4y' + 9y = 0y(O) = 0y(0) = -8Find the general solution of the equation below. y" + 14y' 49y 0...

Question

3. Solve the initial value problem_y" - 4y' + 9y = 0y(O) = 0y(0) = -8Find the general solution of the equation below. y" + 14y' 49y 0

3. Solve the initial value problem_ y" - 4y' + 9y = 0 y(O) = 0 y(0) = -8 Find the general solution of the equation below. y" + 14y' 49y 0



Answers

Solve the initial-value problem.

$ 9y" + 12y' + 4y = 0 $,


$ y(0) = 1 $,


$ y'(0) = 0 $

Hello, everyone. In this human version, we have to find the solution for the initial value problem. The problem is about four wide devilish manners. 20 y dish. Last 25 I It's supposed to zero the initial conditions which are given us. Why did you guys do invited us minus tree like so? First, we have to write the auxiliary question for the essential equations. Sofala squared minus 20 by 20 years. So plus 25 equals judo, so we can light it as to L minus five in the two world minus five, You see quest to Jill like So we get the root says five by 25 by two. Since both the roots are equal. So we had a general form for this equation. That is why is equal to see one April about 2.5 x plus C two x eight to devour 2.5 X Thank you. On this is the general form off Given solution? No, uh, we'll find the whitish well differentiated. So we will get five by two. So you want to get to the power 2.5 x plus five. I do say two x E to the power 2.5 x plus he to the power 2.5 x C two. Right now we just have to apply the initial conditions. That is why you guys to survive. Jesus equals toe. See 18 to the Power Geo plus C two into Ojito. Interview to the power Jeda. So this will give See when it's requested toe like now we will apply the second initial condition. That is why distributor is equal to minus three, which is supposed to five way to see even later the Cultural Plus Five to see toe hated about Jada plus heated about Jesus Ito. So this will give minus three is five by to see one plus Cito, we know the values even is to So we get, uh, see, when I say it was toe plus See too. So this will give the C two s minus eight. Okay, now we just had to substitute the value of C one and C two India General, form off the solution. So we get wise, do we? To the power 2.5 x, my initiate x A to the power 2.5 x site. So this is the solution for the initial value 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. 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.

In this problem, we have to solve the differential equation. Nine. Why? Double prime plus four times. Why is it called a zero? We can always associated characteristic equation Tau this kind of differential equation. So in this case is going to be nine t square plus four is equal to zero. So this implies T square is equal to negative fall off our nine so t is equal to plus minus to over three times. So now we see that the roots of the characteristic equation are complex number. So let's recall the Purim related to complex roots. So it says, if are the one. Is it called to Alfa? Plus I better and our two is it called to Alfa minus. I better art the dudes off the characteristic inauguration. Then the solution that general solution looks like C one times co sign off, Be tykes rusty to time, Stein off Beatrix. And then you have to multiply everything by sea to the power ALF likes. So that's how the general solution looks like. So now in our kiss, we see that Alfa is equal to zero and beat icicle toe to over three. So then that's another solution is going to be. Why is he calling Tau? See one for some constant course. Sign two weeks over three plus C two time sign off twigs over three.


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