Solving Differential Equations with Mathematica's Solver

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Consider the differential equation:

This equation is a very typical separable differential equation. It can be solved by directly integrating both sides, (since it has already been separated.) At least that's what you'd do if you were going to solve it by hand. We're going to figure out how to get Mathematica to do it.

Before we get out the "big guns" let's realize that we can already solve this kind of differential equation with more basic commands than DSolve. What we can do instead is simply mimic with Mathematica the way we would solve this problem if we were doing it on paper! As we mentioned above, this would mean integrating both sides separately, and setting the results equal to each other (up to the obligatory constant, of course.)

Mathematica's Integrate command will do the job for us So let's ask Mathematica for the syntax of Integrate by issuing the command ?Integrate. Go ahead and switch to Mathematica now and try this command. Don't forget to switch back here when you are done.

Let's now move on to discuss the syntax you just discovered.