Plus 1.

That's s times the Laplace transform of f of t, minus f of 0, right?

So we could say that 1 plus v squared is equal to cx.

So let's make v prime is f prime, and let's make u e to the minus st.

And then the right hand side of the equation is this.

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And actually, I'm going to do that right now.

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Repeat this procedure for each particle.

Let me put the Laplace transform of and I'm also going to the sides.

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We figured out what g of 3 was first.

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And now we got that as being equal to this thing, and we made a substitution.

This is equal to 3 times 5, 3 times 5.

And now we can use this, which we proved several videos ago, to resubstitute it and get it in terms of the Laplace

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The chain rule, derivative of cosine is minus sign.

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What was v?

Because we were able to write it as a function of y divided by x.

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So I like to stay away from those crazy Latin alphabets, so we'll just use a regular x.

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From here we can do print 4.

Well, let's do the same idea.

And it's the integral of e to the minus s, but now instead of a t, we have the substitution.

And then from F, there is connection to D and G and those were already in the graph.

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We're going to have to swap 50 down with the smaller of it's two children.

But we're making this substitution that v is equal to y over x.

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