How to Find an Integrating Factor for an Inexact Differential Equation?

heinerL
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Hello

I'm trying to solve the following DGL with an integrating factor:

x'=xg(y)
y'=yh(x)

which is equivalent to -yh(x)dx+xg(x)dy=0 which is an inexact dg?

How to i find an integrating factor in this case?

thx
 
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already found the solution on my own!
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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