No, this makes sense. I actually came up with this stuff like an hour or two ago, but like you said, it looked so simple, I thought that there was no way that it could be right and that I was missing a crucial step and making dumb mistakes like I usually do. Thank you so much for your help. You...
If my math is correct I get
(dx/dy) = k/(2Ky + K^2)^(1/2).
When I differentiated x I came up with
.5((y+K)^2-y^2)^(-1/2)*(2(y+K))-2y
which equates to:
2K/2((y+K)^2-y^2)^(1/2))
Please tell me I did that right.
^I've come to realize that the above is wrong. It should be
x^2 = +,-(y+K)^2 - y^2
I'm still having trouble proving that that answer is the same as
(dx/dy) = (-y+(x^2+y^2)^(1/2))/x
I differentiated the first equation, and came up with (K/((y+K)^2-y^2)) which doesn't relate to the...
Well, I solved/checked it another way and came up with the same answer. What I'm having problems with now is understanding the answer maple gave. My professor gave us a worksheet that demonstrated what the answer was since he was having problems generating the slope fields.
My answer was...
If you come back on and get a chance, you think you could help me with I, more so in see if the answer I obtained is correct.
For Part H I solved it as follows:
x*(dx/dy)^2 + 2y*(dx/dy) = x
w=x^2
.5w^(-1/2)*dw = dx
w^(1/2)*(.5w^(-1/2)*(dw/dy))^2 + 2y*.5w^(-1/2)*dw/dx = w^(1/2)...
So you're saying that dy/dx = cot(theta). I'm sorry but other than that I don't understand where you are going. I can tell I'm over analyzing already. When asking to "derive the relationship" does that simple translate to, state what this means and not literally differentiate?
I understand what you're saying, but my professor never pointed that out. I don't know if it was a typo or if that is how the problem is supposed to read.
As bad as it may sound, I'm having problems understanding part C through E. I've tinkered around with the other portions of the problem, but for some reason, I can't seem to understand those parts. I think I'm over analyzing more than I need to.