I missed the lecture and the text book goes over this very quickly...
This is an autonomous and therefore separable equation so
If I have done this right, what is the next step? If not please correct :$
Thank You
It all is correct so far. Just keep in mind that y is the subject of the equation. So we can rewrite what you have as . Note that if you complete the square, you end up with , where is another constant.
Now, applying the initial condition , we have
Therefore,
Does this make sense?