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The general solution of v +2* # d 1 14r 1 =0 isNone ofitheseolly = (Cli+ Czr + C322) eOi ly = Cer + Cze25loly FE Cl-l(cz + Cx) e...

Question

The general solution of v +2* # d 1 14r 1 =0 isNone ofitheseolly = (Cli+ Czr + C322) eOi ly = Cer + Cze25loly FE Cl-l(cz + Cx) e

The general solution of v +2* # d 1 14r 1 =0 is None ofithese olly = (Cli+ Czr + C322) e Oi ly = Cer + Cze25 loly FE Cl-l(cz + Cx) e



Answers

General solution of $y^{2}+x^{2} y^{\prime}=x y y^{\prime}$ is (a) $e^{\text {dy }}=C x$ (b) $e^{-1 / x}=C x$ (c) $e^{y^{\prime \prime}}=C y$ (d) $e^{x y}=C y$

In this problem we are given that to our In two is a square plus one. The earth. Yes Our par 4-plus 1. The S. Is equal to. Mhm. This is nothing. But who are As a squared plus one. They are close to mine us. Our par 4-plus 1. My dears. This is to R. B divided by minus Our powerful plus one Should be equals two. The S upon I said squared. That's what Now to solve this this part let's take U. Equals two are square. Which means that deal by B. E. R. S. What or who are the R. Is equal to do you. So it becomes deal divided by negative side. You square. Last one is equal to D. S upon As a square plus one. Let's integrate both sides. We get minus talent was of you? Yeah, equals two. Bannon rules of S. Plus constant Q. Or Bannon was of S. Yes. The animals of you Is a constant K. one. This is Shannon was of S. Plus and all of us. R squared is equal story. Yeah. No.

So you have any evidence? Any question or this is equal to de Square Jake. Like it. This five D uh, Let's give you another one Is good Jacobus, kick up. They are a duty. This is brutal thes America. Spiv chacha This cake of they are they're supportive piece where I have this five. Do you could This cake duty center You didn't put the search figured r t is equal and they got some things for the t kept sending. Listen off, DDT Jacob presenting its neikie Kick it. This is ability Cuban three Make it. That's fine. He's going toe. Jacob still kick up. Let's see. How do you see with this? This is Jayendra Shoulders. No replacing out of one musical group. Let's go kick before Yeah, one by three I kept despite by Well, Jacob, this cake up a c is equal. Take this to kick up Step four Say a physical minus from victory Like that. It's one Manus vibrate. Jacob is to minus one. You can This is a good man. Yes. So when this three vehicles Jacob this cake it the search of India's in the mainly because in the huddle do you use a little? Take you by three. I can Has five days square writing Baker is he can get that's management battery. I can the streamer to Jacob this cake up. This is going toe cube by three minus one by three. I kept a five. T scrapped back to another three to Okay, the steepness one. Hey, can This is our off. This is the portable. So there's another given difference in prison.

All right here. We're trying to evaluate our prime tea, uh, equals to be and yet are one equal Stuart W. So v and w are are to constant. That doesn't depend on t. All right, So because they're constantly actually just write the whole thing in in the form in vector form directly. So e r d t was to the soul de are closed to the bt and integrate both sides. And that gives, uh, d r That's just our off the tee, plus a constant vector. So this is a vector now, because we treated the whole thing as a factor. So so let's evaluate our at one. Sorry. Um, are it one is evaluated to be w. And we plug this into there. So we get, um, are in Costa v off we times one plus c equals W. So I see. Um, must be the w minus fee. All right. So deep. The general solution to this equation is thus are comes, equals, stood VT plus w minus the because it

We know determine the solution to this given differential equation. That is uh D two, Y by D X two equals E. Raised to the power of 92 weeks. So to find the solution, I'm going to integrate both sides. When I integrate the left side of that is due to Y by D X two which is basically the second day way too. I will get the first day we do that is dy by dx equals And when I integrate the address to the power of negative works I get a raise to the power of uh minus two works donated by the terribly two of negative works which is basically minus two plus the constant of integration. I put this as simply now I had to live integrate this one more time so that I get the solution in terms of way. So I put this integration symbol for every terms when I integrate the tribute to offer. That is the first today we too I get the function white and this is equal to once again I had to integrate this E raised to the power of negritude works. So I get a raise to the power of negritude works started by I have this negative two already and I will have one more day we two coming from the db two of negative two weeks Derivative of 92 works is basically 92. So this will get multiplied plus integration of CS basically C X. And then we have this another integration constant. The tasty. Now let's get this simplified. So therefore this is equal to E raised to the power of negative two works started by 92 times, offering to two is 4 plus six plus sleep. And this is the solution to the given differential equation, which means option B is correct.


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