Help with understanding a maths solution (1 Viewer)

[Gods_Spear]

I'm trying to solve this question and in the solutions they switch the negative sign I didn't do this and got a slightly different answer ( y = 1 - e^1/2 x as opposed to ) I understand how they got their answer but what tells you that you should switch the signn?

 

[liamkk112]

I'm trying to solve this question View attachment 43505 and in the solutions they switch the negative sign View attachment 43506 I didn't do this and got a slightly different answer ( y = 1 - e^1/2 x as opposed to View attachment 43507) I understand how they got their answer but what tells you that you should switch the signn?

suppose you don’t switch the sign:
you will end up with x = -2ln|1-y| +C by integrating (if you differentiate this, you get -2/(1-y) times (-1) by chain rule so u recover the original function). after this you should end up with the same thing. they just switched the sign to make the chain rule part more obvious

 

[Gods_Spear]

suppose you don’t switch the sign:
you will end up with x = -2ln|1-y| +C by integrating (if you differentiate this, you get -2/(1-y) times (-1) by chain rule so u recover the original function). after this you should end up with the same thing. they just switched the sign to make the chain rule part more obvious

Yeah I'm just dumb, took the integral of 1-y as 1 instead of -1