My online class provided this solution but i have questions about some of the steps. My online professor has been no help. Any input is appreciated.

Question Solve the initial value problem.

Step 1 Separate and integrate

Step 2 Integration result

So where did the

** **come from. I know where the

** **came from but why are they multiplying it by

** **

Step 3 Raise all to the e

Step 4 Result is

Why are they multiplying the right side by

shouldnt it be like this

Step 5

why it the right side now negative?

Step 6

Solution given to us by the professor.

I cant figure out how they arrived to some of those steps maybe someone here can. Thanks.