# Boundary or initial?

• Mar 25th 2010, 05:09 AM
mdruett
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?
• Mar 26th 2010, 02:54 PM
mr fantastic
Quote:

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 ....
• Mar 26th 2010, 07:01 PM
mdruett
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.
• Mar 26th 2010, 09:54 PM
Prove It
Quote:

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.
• Mar 28th 2010, 05:42 AM
mdruett
Thanks
If I knew how to thank, you would both be thanked!
It'll have to be verbal until then!