Question

Find the particular solution of differential equations that satisfies the initial condition
dx/dy=e^(x+y) x(1)=0

I know you have to get all the y and dy on one side and x and dx on the other so you can intagrate and stuff, but im having trouble getting there

Answer 1

dx/dy = e^(x+y)
dx/dy = e^x * e^y
e^-x dx = e^y dy
-e^-x = e^y + c

x(1) = 0, so
0 = e+c
c = -e

-e^-x = e^y - e
e^-x = e - e^y
x = -ln(e - e^y)

Answer 2

Thanks so much!!