Question

In: Advanced Math

3. Consider the IVP: dy =ty^1/3; y(0)=0,t≥0. dt Both y(t) = 0, (the equilibrium solution) and...

3. Consider the IVP:

dy =ty^1/3; y(0)=0,t≥0. dt

Both y(t) = 0, (the equilibrium solution) and y(t) = ?(1/3t^2?)^3/2 are solutions to this IVP.

  1. (a) Show that the trivial solution satisfies the IVP by first verifying that it satisfies the initial condition and then

    verifying that it satisfies the differential equation.

  2. (b) Show that the other solution satisfies the IVP again by first verifying it satisfies the initial condition and then verifying that it satisfies the differential equation.

  3. (c) Explain in your own words why having these two solutions does not violate the existence and uniqueness theorem we discussed in class.

Solutions

Expert Solution

Colby Messinger answered 4 months ago
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