I have run into this problem solving differential equations of this type (they occur often doing momentum problems):(adsbygoogle = window.adsbygoogle || []).push({});

[tex] kxy = (y+dx)(x+dy) [/tex]

where [itex]k[/itex] is constant. I multiply it out to :

[tex] kxy= xy + xdx + ydy + dydx [/tex]

Regroup and :

[tex] \int {kxy} = \int {xdx} + \int {ydy} + \int {dydx} [/itex]

I'm left with the term [itex] \int dxdy [/itex] that I don't know what to do with. Am I able to hold either the [itex]dx[/itex] or [itex]dy[/itex] constant and integrate with respect to the other? I am not able to find a transformation that will remove the [itex]dydx[/itex] or [itex]\frac{dy}{dx}[/itex] or [itex] \frac{dx}{dy} [/itex]. I am also confused about the term [itex] \int kxy [/itex]: integration without respect to a particular differential. How would I solve this differential equation?

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# First order diff eq question

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