Calculus: "Initial Problem" question.

[Soontir C'boath]

I just came back from my exam and this question is driving me nuts.

It's an initial problem that must be solved and it is as follows:

cos(x) = (2y - e^y) dy/dx y(0)=1

First I see it as a seperable equation so it's:

cos(x) dx = (2y - e^y) dy and integrate it to:

-sin(x) = y^2 - e^y

Now, I'm here and I'm thinking I need a solution of a function y, but as you can see, there doesn't seem to be a way to solve for it with e^y unless I didn't learn something important about it. As such, I wrote on the exam that it was unsolvable.

Was I right?

[Kuroneko]

It has no explicit solution, but the implicit solution is sin x = exp(y) - y² + 1 - e. There's nothing wrong with having an implicit solution; it may not be ideal, but it is better than no solution at all.

[Soontir C'boath]

Ahhhhh, thank you, Kuroneko.

P.S. - I like your sig.

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