1. ## Boundary or initial?

1) I have been asked to classify some differential equations as boundary or initial problems. With a first order ordinary DE does this even make sense? There is only one condition to be met y(a) = b

2) If the dependent variable is subject to a modulus operation in one of its terms, does this make the differential equation non-linear?

2. Originally Posted by mdruett
1) I have been asked to classify some differential equations as boundary or initial problems. With a first order ordinary DE does this even make sense? There is only one condition to be met y(a) = b

2) If the dependent variable is subject to a modulus operation in one of its terms, does this make the differential equation non-linear?
1) y(a) = b is an initial condition if a = 0. Otherwise it's called a boundary condition.

2) |y| = y if y > 0 and |y| = -y if y < 0 ....

3. ## thanks, but further clarification req.

1) This is not a time equation necessarily. In second order equations we still have an initial condition problem if y(a) = b and y'(a) = c as I understand it... Does your position remain the same?

2) I understand what the modulus function implies about the value of y. My question is "does this classify as non-linear behavior?" I Suspect yes. It's the definition of a linear equation that I require clarification of, rather than the modulus function.

4. Originally Posted by mdruett
1) This is not a time equation necessarily. In second order equations we still have an initial condition problem if y(a) = b and y'(a) = c as I understand it... Does your position remain the same?
Like Mr F said, it is called an "initial condition" when the value you are given of your independent variable is $0$. This is simply because intuitively this is where we interpret the independent variable as starting. So it doesn't matter if the independent variable is time or not.

5. ## Thanks

If I knew how to thank, you would both be thanked!
It'll have to be verbal until then!