Solving the Preliminary Example
continued fromÌýlast page...)
Your check of equation (2) should look like this:
D[y[t]/.y[t]->E^(3t),t]
3 y[t]+2 x[t]-2 E^(-t)/.{x[t]->E^(-t),y[t]->E^(3t)}
Ìý
Clearly both sides give the same result, making the second equation true when you substitute the proposed solution into it. We have now verified that the proposed solution does indeed satisfy both differential equations in the system. We say that we have foundÌýaÌýsolution of the system. We can't claim that we've found the system'sÌýgeneralÌýsolution, since that would be aÌýfamilyÌýof solutions. What we've found is just a single member of that family.
Let's goÌýand tackle the problem more seriously, puttingÌýMathematica's "big guns" to work.
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