Question: Consider the ODE d t d y = 2 y 1 / 2 Show that the function y ( t ) = 0 is a

Consider the ODE dtdy=2y1/2

  1. Show that the functiony(t)=0is a solution of the ODE
  2. Find a solution for the initial conditiony(1)=1. Limit yourselves to the portion of the solution for which y > 0
  3. Find a solution for the initial conditiony(3)=1. Limit yourselves to the portion of the solution for which y < 0
  4. Combine the solutions from [1-3] to obtain a solution of the ODE that matches simultaneouslyy(1)=1andy(3)=1.
  5. Find a solution of the ODE that matches simultaneouslyy(1)=1andy(4)=1.
  6. We can obtain multiple solutions for this ODE for the same initial conditions y(1) = 1. Explain what is going on in light of existence and uniqueness theorems
  7. Find the general solution for dtdy=2y1/2

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