1. The problem statement, all variables and given/known data Find the exact solution of the initial value problem. Indicate the interval of existence. 2. Relevant equations y'=e^(x+y), i.v.p:y(0)=0 3. The attempt at a solution this is my attempt: dy/dx=e^x+y=(e^x)(e^y) --> dy/e^y=(e^x)dx Integrating, -e^-y=e^x+C (C is constant) --> e^y=-e^x-C --> ln(e^-y)=ln(-e^x-C) --> y=-ln(-e^x-C) Because we have y(0)=0, 0=-ln(-1-C), so C=-2 Therefore, y(x)=-ln(2-e^x) (=ln(1/(2-e^x))) Then, the interval of existence is (0, ln2). This is what i did, but I'm not confident for my work. So I want someone to look at it and help me if you find any mistake. Thanks!