Water was supplied from outside.

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I've just used blue to distinguish the non terminals like this.

And now, we can substitute the derivative of y with respect to x is just this.

We don't know what we're talking about.

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Let's think about ourselves as grape farmers and I'll make a little supply schedule right over here

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

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KIO data supply error.

Jolt, electrify!

Substitution Example

With

So we get v plus x dv dx, the derivative of v with respect to x, is equal to that's just the left hand side it's equal to 1 plus y over x.

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Now let's think about what happens with the number of suppliers.

You could have things like supply shocks.

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So if I see one of these expressions,

There are abundant food supplies.

That's Scenario A.

Maybe to facilitate a laboratory?

What we learn is that if it can be homogeneous, if this is a homogeneous differential equation, that we can make a variable substitution.

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