(a) Find the solution of the initial value problem (b) Determine the interval of existence (i e the largest interval in which the solution is valid) Solution
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[PDF] The Existence and Uniqueness Theorem (of the solution a first order
For an initial value problem of a first order linear equation, the interval of validity, if exists, can be found using this following simple procedure Given: y′ + p(t)y = g(t), y(t0) = y0
[PDF] Lecture Notes for Math 251: ODE and PDE Lecture 7: 24
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 interval of
[PDF] MATH 231, Homework Solutions Part I
(a) Find the solution of the initial value problem (b) Determine the interval of existence (i e the largest interval in which the solution is valid) Solution
[PDF] Math 22B, Homework 3 1 224 &# 1 :Determine and interval in which
1 :Determine and interval in which a solution to the IVP is guaranteed to exist # 8:State the region where the hypotheses of Theorem 2 4 2 are valid for the
[PDF] The Domain of Solutions To Differential Equations - Larry Riddle
The 2006 AB Calculus Exam asked students to find the particular solution y = f(x) to the differential and determine the interval in which the solution is valid
[PDF] First Order Differential Equations Lecture 3
Find an interval in which the initial value prob- lem (3 4) (t − 3)y/ + (lnt)y A valid question to ask now is what happens when the initial equa- tion isn't exact
[PDF] Solutions to Week 2 Homework - Purdue Math
2 fév 2011 · (1) or (2) is valid – the first expresses y as one of two functions of x, the second (c) Determine (at least approximately) the interval in which the
[PDF] Solving First-Order Linear and Exact ODEs
Find the integrating factor: e If you have an initial condition, specify the interval of validity earlier, then only include the part over which your solution is valid
[PDF] What is a differential equation? y′ = f (t)
2 A set of initial condition(s) We first solve the equation to find the general solution (which contains one Step 3: Locate t0 and determine the interval of validity
[PDF] 1 QWA 1 Discuss the existence and uniqueness of - ntc see result
So By Picard's theorem the solution exists and unique in an interval around −1 To find the maximal interval, We notice that the nonlinearity is Lipschitz in domain Now domain of ln is (0,∞), so solution is valid in a domain where e2t < 3 i e
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