# How do you find the validity of an interval

## 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.

## How do you find the interval of an ode?

## How do you find the interval of an initial value problem?

## How do you find the interval of a solution?

## 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:**

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

## What is the T interval in which the solution is valid?

If

**y 0 = 0 − ∞ < t < ∞**is the interval of validity . If y 0 < 0 1 y 0 < t < ∞ is the interval of validity . On a side note, notice that the solution, in its final form, will also work if yo=0 y o = 0 .## What is an interval notation in algebra?

Interval notation is

**a way of writing subsets of the real number line**. A closed interval is one that includes its endpoints: for example, the set {x | −3≤x≤1} . To write this interval in interval notation, we use closed brackets [ ]: [−3,1]## How do you find the interval of increase?

To find the increasing intervals of a given function, one must determine

**the intervals where the function has a positive first derivative**. To find these intervals, first find the critical values, or the points at which the first derivative of the function is equal to zero. For the given function, .## 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)**.## How do you find the unique solution of a differential equation?

## How do you find the maximum interval of existence?

Definition. (Maximal interval of existence ) The interval (α, β) in Theorem 1 is called the maximal interval of existence of the solution

**x(t) of**the initial value problem (1) or simply the maximal interval of existence of the initial value problem (1). x(t) = L ) , then L ∈ ˙ E.## How do you determine if an IVP has a unique solution?

The IVP always has a unique solution

**if f and ∂f/∂x are both continuous in a small rectangle containing x0**.## What does uniqueness theorem say?

A theorem, also called a unicity theorem, stating the uniqueness of a mathematical object, which usually means that

**there is only one object fulfilling given properties**, or that all objects of a given class are equivalent (i.e., they can be represented by the same model).## What is a maximal interval?

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 the largest interval in which a unique solution is guaranteed to exist?

Therefore the biggest interval for which the theorem guarantees existence and uniqueness is

**(3, с)**(note that we are taking the open interval, i.e. excluding the endpoint 3, since the theorem considers open intervals only).## What is differential equation in mathematics?

In mathematics, a differential equation is

**an equation that relates one or more functions and their derivatives**. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two.