Solving ODE via Separation Method: Need Assistance

[Mugged]

Can anyone help me solve this ODE:
..in other words, find a general solution?

dy/dx = e^(x+y)

I use a separation method, but i can't take the natural log of -e^(-y).
So, help?

 

[Filip Larsen]

Perhaps you can move the minus in front of e^-y to the other side of your equation before you apply log.

 

[HallsofIvy]

Looks to me like you have forgotten the constant of integration. You should get something like $y= -ln(C- e^x)$ which exists only for $C> e^x$ or $x< ln(C)$

 

[shelovesmath]

Can anyone help me solve this ODE:
..in other words, find a general solution?

dy/dx = e^(x+y)

I use a separation method, but i can't take the natural log of -e^(-y).
So, help?

e^(x+y) = e^x * e*y
e^(-y) dy = e^x dx
integrate both sides