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:
  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 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.