I didnt check your answer but I would say,
Hello, I was wondering if you guys could quickly check over my work to make sure I did this question correctly. We're solving differential equations using the seperation of variables:
dy/dt = e^(t-y)
(Take integrals of both sides)
I'm not sure if this is right, I wasn't sure how to isolate dy/dt so I put both sides to the power of e, I was just wondering if that was the correct thing to do. All help is appreciated!