Separable Differential Equations

So I have been getting caught up on two separable differential equations the first being:

with initial conditions:

I divided by and multiplied by giving:

and after integrating I got:

and inversing it, so that the u was in the numerator and multiplying by 3 I ended up with:

But I am not sure if this is how the problem is really supposed to be done.

The other equation I am having trouble with is finding the general term for:

where a is some nonzero constant. Would this just be ?

Thanks ahead of time for the help, I really appreciate it.