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.© BrainMass Inc. brainmass.com March 22, 2019, 12:41 am ad1c9bdddf
We will rewrite the equation as follows:
By integrating on both sides, we get:
Now set t to 0 and get:
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
The expert examines the interval of existence of an IVP.