5

4) Halla un operador diferencial que anule la siguiente funcion coS 2x + 3xe 6r...

Question

4) Halla un operador diferencial que anule la siguiente funcion coS 2x + 3xe 6r

4) Halla un operador diferencial que anule la siguiente funcion coS 2x + 3xe 6r



Answers

$$y^{\prime \prime \prime}+4 y^{\prime \prime}+y^{\prime}-26 y=e^{-3 x} \sin 2 x+x$$

Wanna check either. Sets e to the X course sign of two eggs. Andan sign of two eggs if the form of fundamental set of solutions for white prime prime prime minus y prime prime lost four white prime minus for why equal to zero so forced. We check. If the solution, we'd check if the huh this solution. So let's check for eating the eggs. We know that the triple prime of Italy X is also always eating the eggs. The double promise. Also eating the explosives for eating the eggs minus for eating the eggs. This is 1/4 0 So each of the accident solution the last check for co sign of two eggs we have that's white prime will be minus to sign of two eggs we have, that's why double prime because minus for course, sign off Sue eggs. And then we have white chip of prime because it's sign off. So ex. So that implies that's white prime prime. Now maybe it's a sign of soup. Eggs minus white prime prime. I'll be lost because minus miners that was close for your son of two eggs and then lost. Foremost blaming white primes are white primes are minors minus AIDS. Sign off to eggs on the miners for why minus four times co sign of eggs. We'll see that this is also equal to zero. So that's also a solution. And then, lastly, would check for sign of two eggs. In this case, why prime will be Su course. Sign off. Threw eggs. Why prime prime will be minus for sign off to eggs on. Then why chipper Prime? Because a minus is co sign off to X. So that implies, are white people prime, which is minus EADS course. Sign of two eggs minus y parm. Primes are close for sign off to eggs and then lost. Four. White trying Now the it's co sign off to eggs on minus four y minus for sign of three eggs. So this is 1/4. So we see that those two get actually solutions. So next would check if there are fundamental solution. You day. Our fundamental solution fundamental solution on how do we do that? We do that using the Russian. So where you off? So we have to check that and then any independent. So let's look at the Russian off. These not eating the X Co sign off to eggs Sign of two eggs so we find a determinant of beans. Robbie went defensiveness. You are beating the ads when defensiveness. You have minus two son to eggs on the fourth day. Little of this is to co sign off three X The second activities also eating eggs. The secondary is minus four. Co sign of two eggs on the minus four. Sign off through X so we finally determines off days. This will be usually eggs off a complaint on these, but I'll be sine squared off soon. Eggs lost co sign squared off to eggs minus co sign off. Threw eggs off minus four e to the eggs. Sign off to eggs Myers to beat in the eggs. Co sign off eggs and then lost sign of Q eggs off minus four. Eating the eggs off course. Sign of two eggs lost to you to sign off to X. So that means destruction equaled toe Sanskrit. So experts call centers percent square to its supposed to want, so this it's eating the eggs. And then when I explained the rest off loss for into the eggs, sign off to eggs call sign of two eggs lost to eating the eggs cause sine squared off to peds minus for E to the egg sign of two eggs course sign of two eggs and then, lastly, off close to you to the eggs sine squared off two Earths so we can see that this will conservatives on the water off. Let's just be W in court. It's the urge on then off. When you look at these Sunita exits, come on both sides loss. So either the X off sine squared q x lost Corson Sweatsuit Ace. This is also able to one, so they're auction it. Boards are saying you two eggs. This is not to be called zero. We can find out the bones in which this is not identical. Zero. So that is not identical. Zero, it implies dots its forms before them. Intel solution. It's for dumb. It's on set off solution. No, we're not off to solve and find the general solution. Now, George, not question is on. Homogeneous is that homogeneous equation. So let's go back to deeds. Never nimbus the question equal, Shawn one. So you said that sees one is the Virginias question the question the particulate solution. What does zero. What's So the particle lost submission Y p off X equals zero. So ends using equations in Samantha says book, we have that. The general solution general solution is C one eating eggs lost too. Course sign off to eggs. Lost Secretary Simon to X. You're just I didn't constant tow the origin off from that original states and then the laceration zero. So this is the answer.

So for this one we can dividing both sides by ex choir then we'll get throughout you of wipe last you y all were extra see calls to cold sign ex choir or ex choir so we can see this function is certainly in your differential equation and by the integrating factor real how E to the power of just equals two E to the power of to law and X equals two E to the power of law and ex squired equals two X choir so we can times ex choir on both sides of your got expired you have two of y plus two xy just he calls to co sign X choir so we can see the function on the left side jesse calls to the direct T of the function X choir why so if we take integration on both sides you will find expire why on website and integration of coal sign X choir on the right hand so X choir just equals to one plus co sign two X over too bad property the we'll have integration of one hour two Plus integration of course signed two x so one over to you got 1/2 X and for this one we got one over full sign two X we some constant so we know X choir why jesse coastal function like that so we can do a deep outside by ex choir to get the value of why So 1/2 x Signed two axle or for ex choir C O or X choir

But you are going to solve a problem. Number eight. So we have our differential equation for ex spy Our three. Why lost exclusive power for Why best equal. So I'm for three X so we can write it with X power four wide, thus equal sign 243 x so we can get that X wasn't all fourth while equal integrate sign our three x the x so it will be ex support four. Why two great sign x To simplify that I want to play one minus resign squirt x d x So by integration by part method So we can that integration we can write that it's a will be equal Integrate one minus use words minus d you so we have breath, Um, you equal was like X and do you equal minus sign X the X Yeah, so I'll continue. Um, that will be equal. Integrate. Use words minus four minus one d y. So it will be equal 1/3. Why? Why talk about three minus sorry You to the par three minus you plus C so will be equal. 1/3. You multiply used word. My No. Three. Let's see so it will be equal. 1/3 was lying X my by design squirt X minus three plus c So the final solution will the equal, uh, why equal one over B X support four was lying. X multiply design squirt X minor three plus C over X two. So far, four. So thanks for watching. Yeah.

The question is is that we have to find the value for angle X. Here, the question is three into one minus. Synnex is equals to one less cause of two weeks. So now moving towards the solution As we know that one plus caused two weeks, is it close to two causes square X? So three into one minus Synnex can be written as two causes square X. It will be three -3. Synnex is equals two, two into one minus sine square X. And rearranging this equation you will get, it does to sign square x -3. Synnex Plus one is close to zero. So using the midterm splitting method To sin x -1 Into Sine X -1 will be equal to zero. That is from here you will get SIN X equals 21 by two. Or from here you will get SIN X equals to one. So your ex will range from five x 6 or it can be 5, 5 x six or 5 x two. And so this will be the solution to the question. Thank you.


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