finding interval of validity


  • What is the Wronskian method?

    In the mathematics of a square matrix, the Wronskian (or Wro?skian) is a determinant introduced by Józef Hoene-Wro?ski (1812) and named by Thomas Muir (1882, Chapter XVIII). It is used in the study of differential equations, where it can sometimes show linear independence in a set of solutions.
  • What is the interval of existence?

    Due to the previous theorem we can assume that the solution x(t) of (1) is defined on the interval (a, b) where a < 0 < b in such a way that it cannot be extended beyond a or b. This interval is called the maximal interval of existence (MIE) of (1).
  • What is the interval of solution?

    An interval of definition of a solution is any (open) interval on which it is defined. For example: the problem y?=y2, y(0)=1, has solution y(t)=1/(1?t). This solution is defined on the interval (?1/2,1/3), so we can say this is an interval of definition of solution.
  • Identify p(t) and g(t) Find out where p(t) and g(t) are not continuous. List the intervals where both p(t) and g(t) are continuous. From the listed continuity intervals identify the one containing the initial condition, this is your interval of validity.
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