What do you mean by interval of validity domain of the solution of an ode?

Knowing that a differential equation has a unique solution is sometimes more important than actually having the solution itself! Next, if the interval in the theorem is the largest possible interval on which p(t) and g(t) are continuous then the interval is the interval of validity for the solution.

What is the interval of validity?

What is the interval of validity? It is the largest interval of the x-axis which a) contains the initial condition, and b) on which the solution is defined and continuous.

What does interval of validity mean?

Definition of interval of validity For a given differential equation with an initial condition, the interval of validity is the range of values of the independent variable at which the solution to the equation is valid for such initial condition.

On what interval is the solution of the IVP?

Since both p(t) and q(t) are discontinuous at x = ±2, the I.V.P. has a unique solution on the interval (−2,2).

What is the interval of existence?

has a solution existing on some time interval containing t0 in its interior and that the solution is unique on that interval. Let’s say that an interval of existence is an interval containing t0 on which a solution of (1) exists.

How do you find the interval on a frequency table?

A frequency table for a data set containing a large number of data values is constructed as follows:

1. Determine the data range of the data set.
2. Decide the width of the class intervals.
3. Divide the range by the chosen width of the class interval to determine the number of intervals.

What are maximal intervals?

If A is a nonempty open subset of an interval I, then a maximal interval in A is of the form (x, y) ∩ I for some x and y. For instance, if I = [a, b], then a maximal interval in A has the form (x, y), [a, y), (x, b], or [a, b].

What is interval frequency?

Class intervals The frequency of a class interval is the number of observations that occur in a particular predefined interval. So, for example, if 20 people aged 5 to 9 appear in our study’s data, the frequency for the 5–9 interval is 20.

What is interval table?

It is a visual display of data in which equal intervals of data values are shown on the horizontal axis and the frequency associated with each interval is represented by vertical rectangular bars. There are no spaces between the bars of a histogram. You will also learn to organize data by creating a frequency table.

What is an implicit solution to a differential equation?

An implicit solution is any solution that isn’t in explicit form. Note that it is possible to have either general implicit/explicit solutions and actual implicit/explicit solutions. At this point we will ask that you trust us that this is in fact a solution to the differential equation.

How do you find the interval of validity for a differential equation?

Knowing that a differential equation has a unique solution is sometimes more important than actually having the solution itself! Next, if the interval in the theorem is the largest possible interval on which p(t) p ( t) and g(t) g ( t) are continuous then the interval is the interval of validity for the solution.

What is an interval of definition of a solution?

An interval of definition of a solution is any (open) interval on which it is defined. For example: the problem y ′ = y 2, y ( 0) = 1, has solution y ( t) = 1 / ( 1 − t).

What does interval of definition mean in math?

What does interval of definition mean? An interval of definition of a solution is any (open) interval on which it is defined. For example: the problem y ′ = y 2, y ( 0) = 1, has solution y ( t) = 1 / ( 1 − t).