Originally Posted by

**Dudealadude** 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:

e^y(dy)=e^t(dt)

(Take integrals of both sides)

e^y=(e^t)+C

ln(e^y)=ln((e^t)+C)

y=ln(e^t+C)

y(0)=e

e=ln(e^0+C)

e=ln(1+C)

e^e=1+C

C=e^e-1

y=ln(e^t+e^e-1)

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!