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maistral
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If your question is "which is best", the answer is "it depends what ODE you are solving".
 
maistral said:
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That is actually my problem.

I don't know when to use RK4, or when to use ABM. Can someone give me at least general guidelines that will tell me initially i should use RK4 or ABM?
 
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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