Existence and Uniqueness of Solutions: Example1

Example: Suppose the differential equation satisfies the Existence and Uniqueness Theorem for all values of y and t. Suppose and are two solutions to this differential equation.

1.

What can you say about the behavior of the solution of the solution y(t) satisfying the initial condition y(0)=1?
Hint: Draw the two solutions and .

2.

Address the behavior of y(t) as t approaches , and as t approaches .

Solution:

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