Question

Find a solution of the intial value problem.

dy/dx = (e^(x-y))/(1+e^x), y(1)=0

Answer 1

well did you try variable separation method?

Answer 2

I did, and not sure if I am right. But i am at.

y = ln | ln | 1 + e^x | + c |

but it looks wrong to me

Answer 3

hint :\[\large e^{x-y}=\dfrac{e^x}{e^y}\]

Answer 4

you are right !! :)

Answer 5

now use y(1) to get c

Answer 6

what I got was right... okay, so then I would just plug in the 0 and 1 and find c

Answer 7

0 = ln | ln | 2 + e^1 | + C |

Answer 8

umm 0 = ln |2 + e^1| + C

how do I find C, or do I just make it a decimal

Answer 9

C=-ln|2+e|