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Question: 7 24 5 2 pts state where in the typlane...

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7. (2.4, #5) (2 pts) State where in the ty-plane the hypotheses of the Existence and Uniqueness Theorem for First-Order Nonlinear Equations are satisfied for the ODE y = (1-t2-PI/2. 8. (2.4, #18) (2 pts) Consider the initial value problem (a) Verify that yi(t) 1-t and ya(t)/4 are both solutions to the initial value problem b) Explain why does the existence of two solutions not contradict the uniqueness part of the Existence and Uniquess Theorem for First-Order Nonlinear Equa tions 9. (1 pt) The Existence and Uniqueness Theorem for First-Order Nonlinear Equations guarantees the initial value problem ysin(y) (1t)(y - y)4/3, y(0)0 has a solution. Find this solution Hint: None of the methods we have learned so far will work, but try computing y(0) using the ODE and the initial condition. Can you use this to see the solution?
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