MHB Numerical Methods: Second Order Runge-Kutta Scheme

muckyl
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I'm unsure how to begin and solve this question. Any help would be appreciated, thanks.
 

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muckyl said:
I'm unsure how to begin and solve this question. Any help would be appreciated, thanks.

You need to start by writing your DE as a system of first order DEs. Start by writing u = y and v = y'. Can you figure out your system of equations from here?
 
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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