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

  • #1
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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 :/
 

Answers and Replies

  • #2
202
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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.
 
  • #3
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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...
 
  • #4
Mute
Homework Helper
1,388
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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.
 
  • #6
35,132
6,877
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 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.
 

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