Suppose we have y'' = f(t, y); y(a) = y0; y'(a) = y0'(adsbygoogle = window.adsbygoogle || []).push({});

Note all derivatives are with respect to t.

Let u = y', then u' = y''

1. u' = f(t, y), u(a) = y'(a)

2. y' = u, y(a) = y0

Question 1: For y' = u, should I think of this as dy/du = u? Otherwise, I don't see how to solve 2 because what is u as a function of t?

So I pump both (1) and (2) through a numerical ODE solver.

For (1) I get answer u(t), and for (2) I get answer y(t) ? That doesn't seem right, as y(t) is what I want. How do I put my two answers together to get y(t).

As you can probably tell, I'm very confused on this.

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# Second order ODE (numerical)

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