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anonymous
 5 years ago
How do I solve the following differential equation? Thanks.
dy/dx=(1xy)/(x+y)
anonymous
 5 years ago
How do I solve the following differential equation? Thanks. dy/dx=(1xy)/(x+y)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It should be some type of u substitution, we're working on different form of separation of variables.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This is an exact differential equation. You can write it in the form\[(x+y1)+(x+y)\frac{dy}{dx}=0\]Identify,\[M=x+y1\]and\[N=x+y\]Then,\[\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}(=1)\]which shows this is exact. Knowing this, you can move through with solving it.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0In this method, you're looking for a function\[\psi(x,y)=c\]where c is some constant. The proof of the method shows this function should have a form such that\[\frac{\partial \psi}{\partial x}=M\]and\[\frac{\partial \psi }{\partial y}=N\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay this looks good. Thank you, but I think I have to do this using I substitution.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then du=dx and you have\[\frac{dy}{du}=\frac{1u}{u}=\frac{1}{u}1 \rightarrow y=\log u u=\log (x+y) (x+y) +c\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes yes! that's the stuff thank you
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