When y= a constant, how do you find the interval of definition?

[Jeff12341234]

I used the linear equation method to solve a D.E. and got y=3/4 at the end. I'm asked to find the interval of definition but I don't know how to do that when Y is just a constant :/

 

[Apteronotus]

If your solution is y=c then dy/dt must have been 0.
Unless it was specified that dy/dt=0 on some particular interval, then your solution should be valid for all t.

 

[Jeff12341234]

So the interval of definition would be (-∞,∞)?

I just don't get how a function can have a domain when it's just a constant...

 

[Mute]

So the interval of definition would be (-∞,∞)?

I just don't get how a function can have a domain when it's just a constant...

If your function is y(t) = 3/4, it means that for any t you give the function as an input, the function returns the value 3/4. So, the domain is whatever range of values of t you are allowed to put into your function. It doesn't matter that your function happens to return a constant in this case.

 

[Jeff12341234]

thanks

 

[Mark44]

So the interval of definition would be (-∞,∞)?

I just don't get how a function can have a domain when it's just a constant...

Every function has a domain.

If your function is y(t) = 3/4, it means that for any t you give the function as an input, the function returns the value 3/4. So, the domain is whatever range[/color] of values of t you are allowed to put into your function. It doesn't matter that your function happens to return a constant in this case.

I wouldn't use the word "range" when you're talking about the domain, because of confusing the issue with the function's range.