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DE-11 Identify the Y-absent equation.Select one=dy d2y a. G Y, = 0 dx dx2b. None of the other options c. G dy X,Y, d) = 0 dx dx2 dy d. G X; d)= dx dy e. G X,Y, =0 d...

Question

DE-11 Identify the Y-absent equation.Select one=dy d2y a. G Y, = 0 dx dx2b. None of the other options c. G dy X,Y, d) = 0 dx dx2 dy d. G X; d)= dx dy e. G X,Y, =0 dx2

DE-11 Identify the Y-absent equation. Select one= dy d2y a. G Y, = 0 dx dx2 b. None of the other options c. G dy X,Y, d) = 0 dx dx2 dy d. G X; d)= dx dy e. G X,Y, =0 dx2



Answers

Solution for $\left|\begin{array}{lll}\frac{\mathrm{dy}}{\mathrm{dx}} & 1 & \frac{\mathrm{x}}{\mathrm{y}} \\ \frac{\mathrm{y}}{\mathrm{x}} & 1 & \frac{\mathrm{dy}}{\mathrm{dx}}\end{array}\right|=0$ is (a) $x^{2}+y^{2}=c x$ (b) $x^{2}+y^{2}=c y$ (c) $x^{2}-y^{2}=c x$ (d) $x^{2}-y^{2}=c y$

Okay in this problem we have Y equals E. To the X over 10 power. And uh we want to find the differential dy and uh evaluated uh for this value effects and this value of dx Well defined. Dy we have to find dy dx the derivative. No, we want to find a derivative uh of uh why Y equals E to the X over 10. So we need to find dy dx. Now, what is the derivative of E to the X over 10? You can think of X over 10 as let's write it down. You can think of X over 10 As 1/10 times x. So you can think of this as E to the 1/10 times X power. Same thing as E to the X over 10 power. If you want to take the derivative Of E to the 1/10 x. The derivative of E T. D. You is easily you and then we have to take the derivative of U with respect to X. We're using the chain rule. So derivative of uh if this was you derivative of U with respect to X derivative of 1/10 times X is just 1/10. So dy dx is really equal to 1/10 Times E. to the 1/10 x. Or you can rewrite this as X over 10 if you wanted to. But that is our derivative. Now, if dy dx is equal to this, then multiplying both sides by D X will give us our differential Dy because D X divided by and dx being times will cancel. So we have our differential in why is equal to 1/10 times E. Teddy. X over 10. 1 10 times X. We can rewrite as X over 10 time's D. Yet. So here is our differential dy uh huh. Now if we want to evaluate uh dy for this particular X we're gonna plug zero in for X. And for this particular D. X two differential of X. Dx is going to be 20.1 0.1 will replace D. X. Zero will place X. So D. Y. Our differential of why uh for this value X. And this value dx dy equals 1/10 times E. To the X over 10 which will be 0/10. Which of course will of course be zero. Yeah. Uh So 1/10 times he to the 0/10 since X zero times D. X. Which is going to be 00.1. No ah 0/10 zero E. Raised to the zero power. Anything raised to the zero power is one. So D Y is going to be 1/10 times one Times 1 10.1 is 1/10. So D. Y equals 1/10 times one times 1/10 which is 100. Or we could just write it as 1000.1. So our expression for the differential Y dy equals 1/10 times E. To the X over 10 D. X. And our differential. And Y Dy evaluated for this x value and this DX value is .01.

We have to check whether each one is a solution are known. Therefore, the given statement. He's it's Linus minus two y equals judo so faster form. But if we have to check whether this statement is correct for white people's ex Squire, so why nest becomes twice effects. They're full text into wine as minus two y equals X into duets minus. Doing to excess choir is equal to excess while minus drinks Esquire, which is a Pajero. Therefore, we can see that it is up. So listen now, but be where is why equals excuse? Why has becomes three ex Squire, Therefore X, who aren't as minus two y is equal to X into three extra squired minus doing to excuse. This is equal to three x. Q minus two excused equal to X Q. Therefore, it is not a solution. This is dancer to be a problem

Okay, Part A. We know that we can do the question role so one times X minus one minus X plus one times one over the denominator squared. Remember the formulas F one G minus After you won over G squared The simple question negative, too. Over X minus one squared and then we can write a D ax. After this. Maybe wanting to part B. We have negative two over two minus one squared times 0.5 gives us t y equals negative 0.1.

Try to solve these to such problems with the separation of variables and the amount of integrating factors. So first do separation What variables with the 1st 1. And so this is going to give us dy dx Secret to -3 away. So then I have dy over Why is equal to -3 DX integrating both sides here I have the Helena wife is equal to You get three x. Let's see taking a to both sides here I get why is equal to C. E. To the negative three X against that state. First part by suppression of variables. Next this is my p sequel to three and so then have you is equal to to the In a group of three. She goes here to three X. So now I have the already axe of new times, why somebody to three X. Y is equal to zero times 8 to 3 X zero. So integrating both sides here, constant is equal to Into the three x. Y. So not dividing by into three X. Temple sites. Think of why is equal to see into the -3 X. Just the same. Okay. Second problem again, when you do separation of variables first I got T. Y. DT equals to white. Therefore dy over why Is equal to two DT integrating both sides. I get Elena like equals two T plus you. Okay take a nap both sides. I get why is equal to E. To the two T plus C. Here. She calls cE to the to T. That's my separation of variables here. Let's look at the other side now or the method by integrating method of integrating factors. So P is equal to -2. Therefore it is equal to here to the Integral of -2. We'll see you to the -2. X. Sliding that into that. So that's D. Or detox. Let's eat a -2 x. times y. And that's equal to zero Cereal Toast to zero. So then I integrate both sides. Get a constant is equal to It's a -2 x. That's why Divided by eating. They have 2x. to both sides. That ends up flipping that sign there we get like we'll see E. Two the two X. There should be cheers starting with all repair. There should be a team than to hear T. T. T. And we're done.


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