Feb 09, 2017 · 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. By setting the denominator equal to zero, we find that the solution is undefined at and . These two values break the entire x-axis up into three intervals on which the solution is defined (and continuous): .
Jun 03, 2018 · This leads to the following possible intervals of validity, depending on the value of y o y o. If y 0 > 0 − ∞ < t < 1 y 0 is the interval of validity. If y 0 = 0 − ∞ < t < ∞ is the interval of validity. If y 0 < 0 1 y 0 < t < ∞ is the interval of validity. If y 0 > 0 − ∞ < t < 1 y 0 is the interval of validity.
03.06.2018 · 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. This means, that for linear first order differential equations, we won't need to actually solve the differential equation in order to find the interval of validity.
The actual interval of validity is the interval that will contain to = 4. So, the interval of validity for the initial value problem is. In this last example we need to be careful to not jump to the conclusion that the other three intervals cannot be intervals of validity.
09.02.2017 · Thus the interval of validity is . Please comment below if you have questions! Best of luck with the WeBWorK, and enjoy the snow. Regards, Prof. Reitz . Announcements, Resources. homework hints interval of validity. Previous post No classes tomorrow (Thursday 2/9) Next post
The endpoints of each of the intervals are points where at least one of the two functions is discontinuous. This will guarantee that both functions are ...
the interval of validity to the unique solution guaranteed by the theorem. Thus given a ”nice” IVP there is no need to solve the equation to find the ...
In this video we discuss what the interval of validity of an IVP is and how to find it. We comprehensively explain a couple of theorems that give us insight ...
The interval must contain to, but the value of yo, has no effect on the interval of validity. Let’s take a look at an example. Example 1 Without solving, determine the interval of validity for the following initial value problem. TARUN GEHLOT (B.E, CIVIL ENGINEERING, HONOURS) 2. Solution First, in order to use the theorem to find the interval ...
That actual interval of validity will be the interval that contains to = 0. This however, depends TARUN GEHLOT (B.E, CIVIL ENGINEERING, HONOURS) fon the value of yo. If yo < 0 then and so the second interval will contain to = 0. Likewise if yo > 0 then and in this case the first interval will contain to = 0.