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

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Or, we could say, let me just write it the other way.

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Now, since we want to apply this to an integral, maybe

All right.

This expression is just another way of writing this expression.

That means the heap property isn't satisfied but all we have to do to fix it is we just swap the value in the left child and i.

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let's substitute 42 into our original equation

We have 7 minus 10 5.

Everywhere that we saw an x, we will now replace it with a z.

But we could put an x in here.

And if you replace this expression everywhere, where you see an x, right?

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KB OK, swap over positions.

Simple game quest.

But we can figure out what h of 10 is pretty easily.

And now, if we wanted this in terms of x.

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

Well you go back to the definition.

Laplace transform of e to the at.

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There's no trick to it.

Now, we compare the number of 6s with the number of 5s, and there aren't enough.

And we got g of 3 equals 7.

The chain rule, derivative of cosine is minus sign.