Solving Differential Equations with Mathematica's Solver

(continued from last page...)

If you solved this problem "correctly," (yes, I know, there was an error message,) your session with Mathematica should 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 a Solve command wrapped around the equation! But it's not a DSolve command, and the equation inside it is not a differential equation, but an regular algebraic equation. So Mathematica did something, but what?

It essentially solved the differential equation—the output says Solve, not DSolve. In other words the differential equation was solved, but Mathematica was unable to isolate (solve for) y[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 in implicit form. The above answer is Mathematica's convoluted way of giving us an implicit solution. (It's saying that it would like to solve the above, implicit equation, for y[x], but it can't.)

Time to try 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.