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(continued fromÌýlast page...)

If you solved this problem "correctly," (yes, I know, there was an error message,) your session withÌýMathematicaÌýshould have gone something like this:

DSolve[(y[x] E^(x y[x])-1/y[x])+(x E^(x y[x])+x/y[x]^2)y'[x]==0,y[x],x]

Huh? We were expecting to be given a solution in the form of a function as in the previous examples, but look at the above output. There is still aÌýSolveÌýcommand wrapped around the equation! But it'sÌýnotÌýaÌýDSolveÌýcommand, and the equation inside it isÌýnotÌýa differential equation, but an regular algebraic equation. SoÌýMathematicaÌýdidÌýsomething, but what?

It essentially solved theÌýdifferentialÌýequation—the output saysÌýSolve, notÌýDSolve. In other words the differential equation was solved, butÌýMathematicaÌýwas unable to isolate (solve for)Ìýy[x]. You've had this experience many times yourself when trying to solve differential equations on your homework in the lecture part of the class. In these cases we had to leave the answer inÌýimplicit form. The above answer isÌýMathematica's convoluted way of giving us anÌýimplicit solution. (It's saying that it wouldÌýlikeÌýto solve the above, implicit equation, forÌýy[x], but it can't.)

Time toÌýtry another problem...

If you're lost, impatient, want an overview of this laboratory assignment, or maybe even all three, you can click on the compass button on the left to go to the table of contents for this laboratory assignment.