Question

Solve the initial value problem: y'=3y-1, y(0)=0

Answer 1

find y first by the method of integration

Answer 2

integrating both sides I found:
\[y=[e ^{3(C + x)}+1]/3\]

Answer 3

That looks possibly correct. I didn't do it, but you'll get:

ln|3y-1|=x+C