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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# First order diff eq question

**Physics Forums | Science Articles, Homework Help, Discussion**