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5 . Let represent the equation yu? 2ry?u 5yu + 2x where u is assumed to be defined implicitly as function of independent variables € and y: For unique value o...

Question

5 . Let represent the equation yu? 2ry?u 5yu + 2x where u is assumed to be defined implicitly as function of independent variables € and y: For unique value of c > 0, the point (€,y,u) = (3,1,c) satisfies (*). What is the value of Uz(3,1,c)(A) -2/5 (B) 3/5 (C) 2/5 (D) 4/7 (E) -6/5 A number not in (A) - (E) (G) Undetermined because we do not know the value of c

5 . Let represent the equation yu? 2ry?u 5yu + 2x where u is assumed to be defined implicitly as function of independent variables € and y: For unique value of c > 0, the point (€,y,u) = (3,1,c) satisfies (*). What is the value of Uz(3,1,c) (A) -2/5 (B) 3/5 (C) 2/5 (D) 4/7 (E) -6/5 A number not in (A) - (E) (G) Undetermined because we do not know the value of c



Answers

In Problems $5-22:$ (a) Show that each equation is an exact differential equation. (b) Find the general solution. $(4 x-2 y+5) d x+(2 y-2 x) d y=0$

This problem we're going to have um a point to negative 25 Um And we want to find the point that is symmetric. Two it with respect to the X axis, the y axis in the origin. So if we have the point negative 25 it's symmetric with respect to the X axis. We wanted to reflect across the X axis. So based on that the Y axis is going or the y value is going to change but the X value is going to stay the same. So we would have a negative too negative five like that. And if we wanted it to be symmetrical to expect to the y axis we would do the opposite. We keep the five but we changed the negative to positive too. And lastly if we wanted to reflect across the origin we would change both sides so we would have to negative five which would give us this final point.

All right. So we have a number line And it's a -5. All right. If we were going to go to units to the left we could Um subtracts negative too. Right. So I could say negative 5 -2 And we can get -7. Or we could go to units to the right. I could take my negative five add to and that would give me negative three. Yeah. Already. But we want to come up with a solution that will solve for both. Right? So I could rearrange my equations, right? I could move I could rearrange my equations and um Make it a little bit more distinctive to read. So instead of saying negative five minus two equals negative seven. That's the same thing as saying negative five plus seven equals two. Right. I can move this negative two over here and I can move this negative seven to the other side of the equal sign. Just rearranging it. Right? That gives that to by itself. And then you can do the same thing over here. I can move this negative five to the other side, right? And that would give me negative three plus five equals a positive to all right. It sounds weird but just stick with me here. So now I've got this negative five and this positive five. And then I have those variables. We have the negative three and that seven. Remember we're just trying to come up with a solution. Now. Big hint from our answer choices that we're dealing with absolute values. Right? If we think about this, if I have negative five In an absolute equals a positive five, right? So if I created a solution, I could take all of this and say absolute value of five because we're also considering negative five here. And if I add a three or a seven, right, it's going to give me too. Now this negative three is fine because remember we have to consider all values, both positive and negative. So because three or seven is a variable, you could change this to five plus X equals two. So in this case your answer is going to be D.

Even an inequality that is a multiplied by three minus four x plus. C x is less than the multiplied by five X plush toe we have given see is greater than for a plus five day. Now we simplify this vigor. Three A minus for X plus. CXT is less than five b x plus Toby. We aired for a extra both sides and subject. See extra board side and subject. My Toby, we get three. A minor story is less than for a X plus five d x minus E x. This can be written as X multiplied by for a plus five C minus. E is greater than three a miner's toe Be since for a plus fiber T minus, sea is less than zero. That's why when we divide both sides by this vision, the sign up inequality it means X is less than three. A minor story divided by four plus five B minus C. This is the solar son off this inequality

Hi all here. Our question is where is lucy only raised two explicit? The whole square plus C triple A. C four into sine of X plus C. Five. Okay. I think you all can see that the equation is in the fall. What is he gonna do? E ratio X plus C can be a constant. So we have X wherever. So we return as X and B 3% for arbitrary constants. Already conscience on B is constant and it's enough explosive. C can be also written so abc are three constancy arbitrary consensus here, so the order can be three.


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