Homework Help: First order differential equation

1. Jan 12, 2010

Romaha_1

1. The problem statement, all variables and given/known data

Solve the differential equation:

2. Relevant equations

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

3. The attempt at a solution

No idea how to approach this.

2. Jan 13, 2010

HallsofIvy

It looks pretty clear to me. Basic algebra gives
$$x(1- e^{2y})dy/dx= -1$$
and then separate variables as
$$(1- e^{2y})dy= -\frac{1}{x}dx$$

Now integrate.

3. Jan 13, 2010

JFonseka

Hmm, there's an x^2 in the equation, I think you missed that bit.

4. Jan 13, 2010

tiny-tim

Hi Romaha_1! Welcome to PF!

(try using the X2 tag just above the Reply box )

Does putting z = e2y help?

5. Jan 13, 2010

Altabeh

No it doesn't, does it?

6. Jan 13, 2010

Romaha_1

Yes, that's the reason I don't know how to do it. I don't think it is a mistake in the problem, since there is a sign "(very tricky)" after it on the problem set.

7. Jan 13, 2010

tiny-tim

Doesn't it?

8. Jan 13, 2010

JFonseka

The question isn't necessarily wrong, I'm not too good at this stuff at all. It just seemed to me that HallsofIvy was attempting the separable ODE approach, but missed the x^2.

I think it should be:

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

(e$$^{2y}$$)*dy = ($$\frac{1-x}{-x^{2}}$$)*dx

after the separation.

Now you must integrate it. I'm not too sure if I'm right, so be careful.

Last edited: Jan 13, 2010
9. Jan 13, 2010

Romaha_1

Yeah, I understand what you meant and agree with you that the separable approach does not work; it was my assumption that the question was wrong.

10. Jan 13, 2010

JFonseka

I never said the Separable ODE approach doesn't work.

11. Jan 13, 2010

Romaha_1

Sorry, for some reason I could not see the end of your previous post. But still, I do not understnad how this works because the whole expression (x-x2*e2y) is multiplied by dy/dx, not just x2*e2y.

12. Jan 13, 2010

Romaha_1

Hi tiny-tim, thank you for the idea!

But I could solve it only when letting z = x2*e2y; I still do not see how this is possible with z = e2y.

13. Jan 14, 2010

tiny-tim

ah … on this forum, we don't give you the full answer …

so, since you had no idea, I sort-of pushed you half-way (-1 = (x - x2z)(1/2z)dz/dx), and left you to finish it.

having said that, I don't see how z = x2*e2y does it … perhaps i'm misreading the question?