formerlyknownasprince
New member
- Joined
- May 30, 2020
- Messages
- 6
Hi, is the solution to a differential equation a function or a relation?
Thanks
Thanks
Hi, is the solution to a differential equation a function or a relation?
Thanks
That's the difference between a mathematician and an engineer !! [DNE (does-not-exist) and infinity (exists and as many forms)]I disagree with Subhotosh a little on his definition of a function. I prefer to say that a function is a relation with no more than one output for each input.
Another words for a given input you may not have an output. For example, if f(x) = 1/(x-2), then f(2) has not output.
To defend Subhotosh (what am I thinking), he is correct if all inputs come from the domain of the relation.
In general, the solution to a differential equation is a set or family of similar differentiable functions. Typically, you need additional information to reduce the answer to a specific differentiable function, which of course is one element in the set of all differentiable functions, which is one element in the set of all functions, which is one element in the set of all relations.Hi, is the solution to a differential equation a function or a relation?
Thanks
You said:In general, the solution to a differential equation is a set or family of similar differentiable functions. Typically, you need additional information to reduce the answer to a specific differentiable function, which of course is one element in the set of all differentiable functions, which is one element in the set of all functions, which is one element in the set of all relations.
But I find it most helpful to think of the solution to a differential equation in terms of a family of functions having almost identical properties.
I would welcome the comments of Subhotosh Khan and Jomo on this answer.
Who are you calling a mathematician!That's the difference between a mathematician and an engineer !! [DNE (does-not-exist) and infinity (exists and as many forms)]
The gods know I am not a mathematician.Who are you calling a mathematician!
We are keeping that a secret from the students.Everyone knows I am not a mathematician.
thank youHoly smokes! I think the poor OP just wanted to know whether the solution to a DE may be expressed as a relation, to which the answer is "yes". You don't have to be able to "solve it for y".