Interval of existence of an IVP
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Please solve the following problem using the step by step method:
Find the unique solution (and proof that it is unique) and the maximal interval of the initial value problem x' = x^3, x(0) = xo for any xo E R.
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Solution Summary
The expert examines the interval of existence of an IVP.
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ODE Problem
We will rewrite the equation as follows:
By integrating on both sides, we get:
Now set t to 0 and get:
Therefore:
So the solution is
There are two theorems which tells us the fact that the solution exists and is unique.
Theorem 1 (Existence)
Suppose that F(x,y) is a continuous function defined in some region
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Education
- BSc, University of Bucharest
- MSc, Ovidius
- MSc, Stony Brook
- PhD (IP), Stony Brook
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