Question

Find dy/dx for ye^x - x = y^2

Answer 1

start with
\[ye^x+y'e^x-1=2yy'\] and solve for \(y'\) with a bunch of algebra

Answer 2

Eh, I ended up getting \[y' = \frac{ e^{x}+\frac{ y'e ^{x} }{ y }-\frac{ 1 }{ y } }{ 2 }\] I have a feeling this is very much incorrect. xD

Answer 3

I am absolutely horrible at reading all the \frac whatever stuff, but it doesnt look correct xD

Answer 4

I just can't even fathom a way to get that y' on the right hand side out of there. I'm about to just call it quits on this one. ><

Answer 5

Nah, its easier than it looks :P I dont even think of it in terms of getting the y' factored out or whatever. Here is what I do: Everytime I take a derivative of y, I mark it with a dash, just to know thats a y-derivative. After I take the derivative of everything, I gather all my marked terms on one side and put everything else on the other. After that, divide both sides by all the marked terms. It may sound silly, but youre essentially doing the algebra without thinking as hard about it. If it doesnt make sense too much then ill show ya if needed :P

Answer 6

No, no. It makes sense. I'll go back and try with that tack and share my sure-to-be erroneous results. xD

Answer 7

Yeah, sure xD I checked the answer, so Ill let ya know :3

Answer 8

Nope, I'm basically just getting the same thing. ><; It seems that no matter how I situate the terms, I have to turn one side of the equation into a complete mess to simplify the other. Yes. I've decided it just now: I hate this equation. It taunts me, I say!

Answer 9

Ill show ya and hopefully itll help ya with future ones :3