5

Fnd !eiykikanaeEYWE Emi4 MRj +k() WELAV(b) W * W0 # *MNeed HelphHRXEEE...

Question

Fnd !eiykikanaeEYWE Emi4 MRj +k() WELAV(b) W * W0 # *MNeed HelphHRXEEE

Fnd !eiykikanaeEY WE Emi4 MRj +k () WELAV (b) W * W 0 # *M Need Helph HRXEEE



Answers

$w^{\prime \prime}+w=u(t-2)-u(t-4)$ $w(0)=1, \quad w^{\prime}(0)=0$

Okay, So for this program were student that the solution today? So the w Because the power Siri's expansion, which is some mission que from zero to infinity a k now Xscape. And once we have this assumption, we can ride out the first of the curative off W into the second. The purity of off w like this just take a majority of time by term. Okay, so we plugging this three functions into the OD left inside because Teoh the submission k from two to infinity, que times k minus one a que extra extra K minus two minus play from 1 to 70 10 times a k times x tree K pass one in the past estimation K from zero to infinity a que Xscape. Okay, so we only need to write out a couple of different terms. So, for example, a constant home. And so we look at off these three terms circular constant. We have, um, a zero press twice off a two in the full a linear term. If we collect, um, the linear terms from off these three. We have a one class six a three times X in the process arrest. So risk terminal be higher or the terms. So this is 11 site on the right hand side. Causes your land means everything on the left will be zero. Let me is the constant term zero, which gives us a two will be minus one Have a zero. The linear term of zero. That means the coefficients off list in your term. The one plus six a three course zero, which is which gives us a three close to minus 1/6. A one. Okay, so, um, since we only care about the first for non zero turns, so w b close to zero process a one x minus one. Have a zero x square, minus 1/6 a one X cube, plus Ah, higher order terms. Okay. Also, that it's This is a solution for this property. This is the first for a non zero terms.

For this program, we first assume that the solution to this so the W has a policy Ray six expansion. With this assumption, we can ride out the Garrett tears off taboo eso we packing these three functions into the OD deaf in society close to submission K from two to infinity que times k minus one a que ext became minus to plus summation K from one to infinity three k a k extricate minus que because it zero to infinity a que extricate so we can collect, um, the same or their terms. So, for example, a constant we have to a two front miners a zero and we know this constant has to be zero. It gives us a two week close to ah, why have of a zero in the linear in your term, we have six a three miners twice off a one equals zero. It gives us a three close to minus 1/3 off a zero so we can stop here for a little off for a while because we have some initial conditions. So the initial condition directly gives us what's easier. And what's a one so easy are requested to and they won t close to zero. With this initial conditions, a two will be one. A three will be zero. Okay, so, um, this rewrite this left inside in the following way. So we have with splitter first term into twice off a two plus six a three x cross summation que from four to infinity K times K minus one. A k x two became minus two in the full of second term. Should be three a one x plus the rest and for last term is minus a zero minus a one x minus. Submission que From two to infinity A k Xscape. Um, so we collect the same terms and by shifting the index for this so we can shift the index for this particular term. So the new index would be K for all the summation k from two to infinity. So the starting point is decreasing by two. That means everything inside will increased by two. So as we make this shifting, we are able to merge off the summations into one. So the summation will be K start off run two to Infante, e K plus two times, Cape Cross one. Hey sub k plus two crossed, three K K minus a k Times extricate. And we already discussed the 1st 2 terms and that this turn gives us a recursive relation. Eight. Case plus two equals to one miner's three K over K plus two times K plus one face up cape. Okay, so we know that a zero because two to a one you close to zero and a two week cost. One a three course zero and for a four before if we bragging K Coast to to into this recursive relational before he caused to why number 12 A to minors six. A two now gives us minus five off 12 A. To So before you cause a four ecos toe minus five over tough a five equals zero because a five equals or something times a three a six equals Teoh. So when Katie cost before, we have 30 on the denominator and the miners 11 times a for So we have a six. He caused toe 11/72. Okay, so that means the first of non zero terms for this function, w will be two plus x square miners five or 12 extra fourth power plus 11/72 x 36

You used to fight toward up by the legs then Bernardo, by no way then don't of you. But do is there the function is Do you get a polar? That play? You're saying off heads, remember, you minus does a square. The blue bless work equals zero. So first we need to find affordable by blacks. It is it's number. You you can go available on its way in Dubai. Yes, into the polar. It's like into course it's W India. No, the real. But publics might as that square, I don't know, but Bill s equal to zero. Who if you take the Lord of your bagel X over, they can sort it like why it would about pick flight in beside heads and w they're quit. Why does available are excellent. It go calls head to w be part of the business. When it looked like a big old it'll be like side. It's a w it do into the parlor explain into pigs. Plus, he did a bar X like in tow calls to w you do notably obey bill like, but it does. They're squared and do Dorda bill by it all y equals zero so no w by no lady if your tape calm and we will get like minus side Head said that you know, eggs. You did a lot of excellent David Obey evil about it perfectly into course, hitching a B minus there quick. Then the partner took was noticeable. That break elicit opiate bagels that function real bigger. Can you play? It is to explain in group Cools it's a number you into report a bill, but music minus was that square and that would a bill by Bill. Is it my life rules that equal Brazil? So, Lord of Real Baby Bill, is it Indo here in the bar Exley finger? Because hated Abreu by just is that square tickle toe bruise that w so Berta blew by those that you could do. Who's that? W door. But you dicks to Pixley course. Heads of embryo minus Does that question

You used to fight toward up by the legs then Bernardo, by no way then don't of you. But do is there the function is Do you get a polar? That play? You're saying off heads, remember, you minus does a square. The blue bless work equals zero. So first we need to find affordable by blacks. It is it's number. You you can go available on its way in Dubai. Yes, into the polar. It's like into course it's W India. No, the real. But publics might as that square, I don't know, but Bill s equal to zero. Who if you take the Lord of your bagel X over, they can sort it like why it would about pick flight in beside heads and w they're quit. Why does available are excellent. It go calls head to w be part of the business. When it looked like a big old it'll be like side. It's a w it do into the parlor explain into pigs. Plus, he did a bar X like in tow calls to w you do notably obey bill like, but it does. They're squared and do Dorda bill by it all y equals zero so no w by no lady if your tape calm and we will get like minus side Head said that you know, eggs. You did a lot of excellent David Obey evil about it perfectly into course, hitching a B minus there quick. Then the partner took was noticeable. That break elicit opiate bagels that function real bigger. Can you play? It is to explain in group Cools it's a number you into report a bill, but music minus was that square and that would a bill by Bill. Is it my life rules that equal Brazil? So, Lord of Real Baby Bill, is it Indo here in the bar Exley finger? Because hated Abreu by just is that square tickle toe bruise that w so Berta blew by those that you could do. Who's that? W door. But you dicks to Pixley course. Heads of embryo minus Does that question


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