Green Functions: Solving Inhomog. ODE's with Ease

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What is the advantage of using Green Functions to solve inhomog. ODE's?
 
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I think that its principal advantage lies in its portability. If you get the Green's function for a particular configuration of a system, then that same Green's function can be used no matter what the source term is in the inhomogeneous DE.
 
Tom Mattson said:
I think that its principal advantage lies in its portability. If you get the Green's function for a particular configuration of a system, then that same Green's function can be used no matter what the source term is in the inhomogeneous DE.


The source term corresponds to the RHS of the equation right?

(In general)
 
That's the standard convention, yes.
 
Ok, thanks for clearing that up for me!
 
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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