Exact vs. Non-Exact Differential Equations: What Sets Them Apart?

Gear300
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What is the difference between the behavior of solutions that are exact and those that are not?
 
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As far as I know, the solutions don't have any special properties.

Describing an equation as "exact" just means it is easy to solve using a particular technique (i.e finding an integrating factor).
 
Oh...I see. I don't really see anything too special in their phase portraits either. Thanks for the reply.
 
There is no difference in the solutions- every "non-exact" differential equation can be made into an exact equation, with exactly the same solutions, by multiplying by an "integrating factor".
 
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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