Solving Differential Equations with Mathematica's Solver
(continued fromÌýlast page...)
Consider the differential equation:
This equation is a very typicalÌýseparableÌýdifferential 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 getÌýMathematicaÌýto 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 thanÌýDSolve. What we can do instead is simply mimic withÌýMathematicaÌýthe 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'sÌýIntegrateÌýcommand will do the job for us So let's askÌýMathematicaÌýfor the syntax ofÌýIntegrateÌýby issuing the commandÌý?Integrate. Go ahead and switch toÌýMathematicaÌýnow and try this command. Don't forget to switch back here when you are done.
Let's nowÌýmove onÌýto discuss the syntax you just discovered.
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