MarkFL said:I can see why $x=0$ is eliminated in order to write the ODE in the form:
\(\displaystyle \frac{d}{dx}\left(\frac{y}{x}\right)=\sin(x)\)
But I don't know why they have restricted $x$ only to positive values. :D
find_the_fun said:Isn't it because interval has to be continuous i.e. can't have a break at 0?
The interval solution is determined by the specific problem being solved and the available data. It is a mathematical representation of the range of possible values for the solution. This range is often necessary due to uncertainty or variability in the data, and it allows for a more accurate and comprehensive understanding of the problem.
A single point solution is a specific value that is determined as the best or most optimal solution to a problem. It does not take into account any potential variability or uncertainty in the data. In contrast, an interval solution considers the range of possible values and provides a more comprehensive understanding of the problem.
Yes, the interval solution can change depending on the data used. As the data is the basis for determining the range of values, if the data changes, the range and therefore the interval solution may also change. This is why it is important to carefully consider the data and its accuracy when determining an interval solution.
The confidence level for an interval solution is determined by the level of certainty or probability assigned to the range of values. This can be based on statistical analysis or expert judgement. A higher confidence level indicates a greater certainty in the interval solution.
An interval solution can be used to make a decision, but it is important to consider the level of uncertainty and variability in the data. The interval solution may provide a range of possible outcomes, so it is important to carefully weigh the potential risks and benefits before making a decision based on the interval solution.