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In this problem, we construct several solutions to a single IVP. This would contradict the existence and uniqueness theorem if the hypotheses of that theorem were satisfied (luckily, they aren't): Consider the initial value problem: y(t) = y(0) There is a constant solution to this IVP. Find it. For the same IVP as part (a), is there a continuously differentiable solution at t = 0? If t > 0, y(t) = t; if t < 0, y(t) = 0. Find the non-zero constant for which this is a solution. Consider the initial value problem: y(t) = Vyy(0) There is a constant solution to this IVP. Find it. For the same IVP as part (c), is there a continuously differentiable solution at t = 0? If t > 0, y(t) = t^2; if t < 0, y(t) = 0. Find the non-zero constant for which this is a solution.

          In this problem, we construct several solutions to a single IVP. This would contradict the existence and uniqueness theorem if the hypotheses of that theorem were satisfied (luckily, they aren't):

Consider the initial value problem:
y(t) = y(0)

There is a constant solution to this IVP. Find it.

For the same IVP as part (a), is there a continuously differentiable solution at t = 0? If t > 0, y(t) = t; if t < 0, y(t) = 0. Find the non-zero constant for which this is a solution.

Consider the initial value problem:
y(t) = Vyy(0)

There is a constant solution to this IVP. Find it.

For the same IVP as part (c), is there a continuously differentiable solution at t = 0? If t > 0, y(t) = t^2; if t < 0, y(t) = 0. Find the non-zero constant for which this is a solution.

3 points in this problem we construct severa solutions t0 single ivp this would contradict the existence and uniqueness theorem if the hypotheses of that theorem were satisfied luckily they 41998

Added by Joyce M.

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