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7. Y1' =2Y1 - Yz + Inx Yz' = 4y1 - 2Y28. y" - (3 cotx)y' - Zy=0. Note that Y1 = cos xis one solution....

Question

7. Y1' =2Y1 - Yz + Inx Yz' = 4y1 - 2Y28. y" - (3 cotx)y' - Zy=0. Note that Y1 = cos xis one solution.

7. Y1' =2Y1 - Yz + Inx Yz' = 4y1 - 2Y2 8. y" - (3 cotx)y' - Zy=0. Note that Y1 = cos xis one solution.



Answers

Find $d y / d x$. $$ y=-2 \cos (-3 x+7) $$

In this question we have to solve or given the potential equation that is divide where the X. His. It was too three cause to works let's to sign to the X. And the given condition is Why why why to it was 28. No we can write the situation is the why is it was 23 post two works Let's to sign three x. And multiplied wife PX. Now we integrate yet on both the sides and after integration we can see here we get by the close to three into Signed two works by two and -2 into Signed three x by three. Let's see now we can see we need to find the value of this constancy and for that we are given with the condition that why Bye bye to because to eight it means that If excess by by two then why is it was 28 substitute this value here. So we see we got here it is it was 23 by doing two signed by and minus two Y. Today into sign trip by way too. Wait a while you can see here integration of chinese course so due to the citizen I had to right here of course. So for three years by three. No we substitute the value here. So here we have to write course so this is of course three by way too. And let's see now we can see it value of signed by zero and value of course three by but it is also zero So we got 30 that was too they don't mind a zero. Let's see the value of C. Is eight and now substituting this value. I can say that I get the required solution of this differential equation. That is why is it was true three x 2 signed to works -2 Way three cost 30 X plus eight. This is the of the given question here. Thank you.

It's already converting from spherical two rectangular. So it's important to note that there is a conversion for this, we're gonna have X equals row, which right is p sign fee code saying there you go. And then why is going to equal rho times sine fee signed data and then z is going to equal roco saying feet. So we're going to use these equations to answer all of our other equations with the given points. So for example, if we're given 45 or six power before there is just an example but we can see this with any problem that's given to us. We would end up having x equals four times the sign of number four which is route 2/2. I'm the code sign pi over six Which is going to be route three over to. That's going to end up giving us route six as we sit here. And then why is going to be four Times The sine of fee? Again, that's going to be rude to over two and then we're going to have times sine of data which is going to be one half. So really that's just gonna end up being rude to because we have the fourth, so this one has so Can you cancel and that's just going to give us route two And lastly we'll have Z which is going to equal Uh four times the co sign of the so that's for times route you over to and that ends up giving us to route to as our final answer

Our ultimate goal for this set of problems is to find an equation in spherical coordinates given the rectangular coordinates. So it's important to remember that um were given rectangular and we're trying to go to spherical. So what that tells us is that we have um Y equals two. That's it. That means x equals zero And z equals zero. So when it comes to finding row we know that rho squared is equal to x squared plus Y squared plus Z squared, but x squared, Z squared are equal to zero. So we really just have that row equals Okay, and that's going to be our problem to that. That's gonna be a result That we can consider other possibilities such as E equals six. If we end up getting something like z equals six then similar to what we had before, that's just going to end up telling us that row is equal to six because everything else is equal to zero, then we can consider other possibilities such as um expert. Plus y squared plus Z squared equals 49. We already know that again, rho squared is equal to x squared plus y squared plus Z squared. So row itself would be equal rho squared. We see as 49 That tells us that row is just equal to seven. Um These are all really good ways of showing this. We can also do other options um such as expert. Um Plus widespread equals 16. So we can combine other components knowing the X squared. Um since we know that X is row signed, the coastline data and why is roast sign the signed data? We can combine terms and end up getting our final answer.

With this question were given a public warning. It's ours equals a 3/3 minus closer data. When were asked to change these into acting recorded. So to start off with the most part most guys were three MySQL Cynthia to get us. We are my street close on. Data is equal to three. Next week. In fact, are three ts three. My three times are mice. Customer data equals two or three. My best as by three tiers are mice. Custom data is equal to one. We can see we can most. Why are straight across the board? Two years are squirt nice. Arcosanti data is able to our which will get us X squared plus y squared minus X is equal to the square root. Uh, let's see X squared possible. I scored. I don't see a next thing could do. Yes, we could at sea. So export post Bisquick. So the next thing we do is we could square everything, Ashley. But still you square eight And so then we square Besides against expert post y squared, you know, our side was really must've extra four plus two x squared. Why squared close allies to the fourth minus two x cubes, most to ex wife's word. Mm, that's just so little war. Oh, plus X squared. So then let's see if we can have X words can't outs and their wife's words cancel. Oh, it's see you should have. We'll have the wife's words and you just have exports. Cancel out to leave us with exit 1/4 plus to our scored y squared plus y to fourth My Mr X cute minus shoe X Y squared minus y squared is equal to zero.


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