Solving the Preliminary Example
continued fromÌýlast page...)
Your latest session should look like this:
y[t]-x[t]-E^(3t)/.{x[t]->E^(-t),y[t]->E^(3t)}
which tells us the value of theÌýright hand sideÌýof equation (1). Comparing this with what we got on the previous command for the left hand side, we see that they are the same. So far, so good. Substituting the proposed solution into both sides of the equation yields the same result, i.e. renders the equation aÌýtrueÌýstatement. All we need to do now is check to see whether our solution works on theÌýsecond equation.
We check the second equation in the same way that we checked the first, by making substitutions into both sides individually, and checking to see if the results are equal. The commands required are very similar to the ones we just made, so I'm leaving it up to you to check the other equation. (It will takeÌýtwoÌýcommands, remember.)
Well don't just sit there, go back toÌýMathematicaÌýand get on with it! Come back here when you're done.
°Â±ð'±ô±ôÌýnow seeÌýwhat you should have gotten...
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