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!