"Five minutes"?

That is anextremelybig question.

Not all differential equations have solutions that can be determined analytically. In fact the vast majority can't be.

The ones you're likely to get in an introductory course will be carefully taylored (deliberate pun) to fit the techniques which you will be guided through one by one. Some d.e's are solvable using easy techniques, some by more difficult ones.

This one:

looks at first glance to lend itself to an integrating factor approach, but this is an area in which I'm rusty and would need to check. You may be able to separate the variables.

Your five minutes are up, I'm afraid.