(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Solve for either x or y:

[tex]\frac{dy}{dx} + \frac{dx}{dy} = 1[/tex]

2. Relevant equations

I don't know any.

3. The attempt at a solution

Let

[tex]y' = \frac{dy}{dx}[/tex]

so then the problem becomes

[tex]y' + \frac{1}{y'} = 1[/tex]

[tex]y'^2 + 1 = y'[/tex]

[tex]y'^2 - y' + 1 = 0[/tex]

So then I thought, why not use the quadratic equation? I get

[tex]y' = \frac{1 \pm \sqrt{-3}}{2}[/tex]

And indeed, adding this to its reciprocal gives a sum of 1:

[tex]\frac{1 \pm \sqrt{-3}}{2} + \frac{2}{1 \pm \sqrt{-3}} = 1[/tex]

What does not sit well with me, though, is that complex numbers are involved. Is that allowed? Furthermore, would y = Ax + C be a solution (where A is the complex number from two lines up)?

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# Homework Help: Dy/dx + dx/dy = 1

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