Okay lets see if someone on here can help me. This problem looks pretty easy:
I see that its an autonomous equation that will allow for separation of variables, which I do. I separate and integrate accordingly which yields me:
now I raise each side exponentially to get rid of the ln's:
this is where I think I am making a mistake. There must be some law of logarithms that I don't see because the answer turns out to be (according to the back of my book):
I can only come up with the ce^t and the rest is wrong. Can someone fill me in to what I need to do/what I am doing wrong?