It's zero.

Let's substitute y of 0 here. y of 0 is 2, so s times y of 0 is 2 times s, so 2s, distribute that s, minus y prime of 0.

They say y of 0 is equal to 1, and y prime of 0 is equal to 0.

Then we have the absolute value of zero.

Deflection does not return to zero.

A value of 0 disables the timeout

Y prime of 0 is 3.

I'll do it in orange, they tell us that y of 0 is equal to 0, and y prime of 0 is equal to 0.

And then it would go back to zero and then go like that.

This approach 0, so we're not sure.

What is f prime of 0? f prime.

No, sir. I haven't got anything to whistle about.

Transform of y, so plus 5s times the Laplace Transform of y, minus 5 times y of 0. y of 0 is 2, so minus 10.

Our initial condition is y prime of 0 is equal to 0.

Second initial condition was y prime of 0 is equal to 0.

If we just put here change in x is 0 you are going to get something undefined.

Well that's s times the Laplace Transform of y, minus y of 0, right?

At time is equal to 0, this term cancels out, where x is equal to 10.

When T is zero, the field equation describes empty space (the vacuum).

So it bumps it up.

We just take the slope at some point and find the limit as we take the difference between the two points to 0.

And since we borrowed that 1, this 2 will become a 1. We took 1 away from this 2 and we gave it to the 0 to make 10.

And the initial conditions are y of 0 is equal to 2, and y prime of 0 is equal to 3.

When t is equal to 2, you get the Dirac delta of zero, so that's where you would have your spike.

And if you had a strong acid, not a strong base, you would end up with a pH of 0.

zero, we don't get three.

So, count equals zero. Then, inside of the loop, inside the if statement, where, you know, I, I print the row as we've done many times before.

So count is zero and then it gets to this line. So the first thing it's going to do is evaluate the right hand side.

So when the spring is barely compressed, we're going to apply a little, little bit of force, so almost at zero.

Part B. For x is not equal to zero, express f prime of x as a piecewise defined function.

So minus y prime of 0 and now I'll switch colors plus 5 times once again the Laplace Transform of y prime.

The Laplace Transform of f prime, or we could even say y prime, is equal to s times the Laplace Transform of y, minus y of 0.

So we get s squared, times the Laplace Transform of y I'm going to write smaller, I've learned my lesson minus s times y of 0.

It has to have a second derivative of 0, and when you go above or below that x, the second derivative has to actually change signs.

Finally, it is not even clear that the zero lower bound is primarily responsible for high US unemployment.

Because I was in the hospital after, I think it was my fourth round of chemo when my numbers went to zero, and I had basically no immune system.

Well, this unit step function, when we pass pi, is only going to be equal to 1, but we want this thing to be equal to zero.

So 5 times s times Laplace Transform of y, minus y of 0, plus 6 times the Laplace Transform oh I ran out of space, I'll do it in another line plus 6 times the

Automatic

The derivative of y with respect to x is equal to y cosine of x divided by 1 plus 2y squared, and they give us an initial condition that y of 0 is equal to 1.

For t is greater than or equal to 0, the derivative of x with respect to t is 4t 1 the derivative of y with respect to t is sin(t 2) and at time t 0, x(0) 0 and y(0) 4

By selecting the center of gravity as the reference point for a rigid body, the gravity forces will not cause the body to rotate, which means weight of the body can be considered to be concentrated at the center of mass.

16 2 18, and then that is equal to x over 4 (X 4) x over 4 and then we have 2 2, which is just going to be zero, so we don't even have to write that.