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I have run into this problem solving differential equations of this type (they occur often doing momentum problems):
[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] <br /> <br /> 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?[/tex]
[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] <br /> <br /> 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?[/tex]
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