Consider the initial value problem.It is not difficult to construct an infinite number of...

Consider the initial value problem

.

It is not difficult to construct an infinite number of solutions. Consider

where t0 is any positive number. It is easy to calculate the derivative of y(t), when t ≠ t0,

but the derivative at t0 remains uncertain.

(a) Evaluate both

and

showing that

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(b) Finally, show that y(t) is a solution of 21. Why doesn’t this example contradict Theorem 7.16?