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XCesLelxAdy=Ena 4+xcos 9 )ax_ xdy =0 24LZlol09zg Ysl r8503 ( @lyssa Asjai 0 AcLiis...

Question

XCesLelxAdy=Ena 4+xcos 9 )ax_ xdy =0 24LZlol09zg Ysl r8503 ( @lyssa Asjai 0 AcLiis

XCes Lelx Ady= Ena 4+xcos 9 )ax_ xdy =0 24 LZlol 09zg Ysl r8503 ( @lyssa Asjai 0 AcLiis



Answers

24. $$y^{\prime \prime}-9 y=g(t) ; \quad y(0)=2, \quad y^{\prime}(0)=0$$

Solve the equation, then check the solution. Nine A equals zero to isolate the variable. Undo the product using division. Divide both sides by nine zero. Divided by nine is zero a equals zero. To check your solution, substitute zero into the original equation for a and see if it's a true statement. Is nine times zero equal to zero nine times zero is 00 is equal to zero A equals zero is the solution.

Case of the first problem here says Negative. Nine. Divided by three equals negative three. Well, that's because three times native three is equal to negative nine. Okay, Part best party. Don't be zero divided by 80 because eight time zero is equal to zero, okay?

So here's our interval here. It's from four nines to 4/7 and 40.5 is our ex, not value. So that means that if we pick a value, say, like 0.52 that is inappropriate Delta value because it's within the interval and it's not equal 2.5.

So here we have our question, which is vital Prime plus nine wise it was to Do you have tea? I have serious equipped to and why Prime of zero is equal to negative three. And you need to take the place of this equation. Now it's rised about that. The clasp Oh, the second derivative is equal to the first function Y ve assumption of s into s squared Subtract why of zero well deployed by us and subtract Why prime off through? So this is a format for the class of the second derivative and then the placebo. Just a single where you pull y my team. This case is equal to So why is a function? Let's put these two back into our equation. So enriching little pacifist equation that you first drink comes to be It's weird. Into y is a function of s subtract Why it zero which in our case is too We'll just write it out too shut too multiplied by s try Why prime of Syria, which is negative and add nine multiplied by adult plus a why Which is why this why which equals a plus. She too And this we can rewrite it as another function supposed ex as a function of this hurry. So no, you know that. Why was this going in these two terms? You could take that a squared plus nine multiplied by by a bus and we can and send these to germs to the right hand side. So because exit s plus two s minus and to isolate why thus we divide the right and side by escort studio here, so the full term is, but that's it. Two to s divided by a squared plus nine my history by a square plus nine and expose this divided by a squared but thanks. And so and let's go back to our contents. No, that that the plus of the treatment, your function cause of a constant multiplied by a very able T schools, as in the denominator by by the constant squared That's s squirt. And we know that a classic sign T is equal to the constant in the new meter. But by constant square, when we think the inverse of this side the right hand side, these two equations we come up with cause of the constant most primary variable and signing the costumer by regrettable were just shifting. Bill plastered this side which makes it Bill plus in. So when you take the plus in words of this whole equation here we end up with the plastic in were supply of this which is no past members. Why, EVs would be by Ft. So the passengers of flight of us do Why t well to go plus in worst. So this room which is two multiplied by s over a squared plus night. And when you look at this the right hand side this term, my cure, it's the same format. We can rewrite nine as three squared. So that would make b r. That that would make be the equal to three. So we can rewrite a CZ cause to e t and then subtract this true. It's similar to this room right here were signed Bt and in the numerator we have three in the denominator week Invite nine is three square so this could be rewritten us sign Oh, three tea plus the clasp in worst all except s multiplied by one over s squared this nine and this is the multiplication two functions. So let's focus on this whole term right here and all of them in Utah. It's a little plus in worst. Oh, except s. It's equal to still plus inverse of number will be replaced The G o Philip, last of G of tea with ex service Let's put that back in until a plus in words and the class cancel each other out. So we just end up with a G ft. This is our first function when we take the bus in words of won over s squared plus nine, we could be right this as sign three tea if we had three in the numerator but we don't. So in order to make there be a three in the numerator well, multiply and divide it by three. So this gives us signed three t But we're left over with the three and the denominators so divided by three. And this is our second function justice now by the convolutions formula, you know that pelvis into G of us and two functions are being multiplied together in tow when we're using the convolutions form that we end up with into girl from zero T Oh, variable talk, talking be any variable other than tea into G O. This is the second function G o t minus talk into D talk. So in our case, that supposed that tall is why so we'll replace this tea by why, and we'll replace this TV here by way. So our first function, we just write that as is so the integral from zero t first function is g off and we will write it as our toys wise g a y multiplied by the second function which is sign oh three now T is why, but you hear we have to write. It s t minus tall and her Why is tall so we can write it as t minus Why divided by three multiply by t. Why? So Regan replaced this whole term into this equation right here. And we end up with why of tea is equal to to cause three tea minus sign 32 less the integral of zero t sign three t minus. Why bye bye Multiplied by the second function which was to you, why multiplied by get it? It's severely multiplied by d o. What. So this whole term is our answer. I hope that my tents


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