Question

For each of the initial conditions below, determine the largest interval a < t < b on which the existence and uniqueness theorem for first order linear differential equations guarantees the existence of a unique solution.

y(-7) = -5.5



y(-0.5) = 6.4.



y(0) = 0.



y(5.5) = -3.14.



y(10) = 2.6.

Answer 1

The largest intervals on which the existence and uniqueness theorem guarantees a unique solution for the given initial conditions.

Step-by-step explanation:

The interval a < t < b on which the existence and uniqueness theorem for first order linear differential equations guarantees the existence of a unique solution depends on the initial conditions. For the given initial conditions:

• y(-7) = -5.5: The largest interval is from t = -7 to t = -0.5
• y(-0.5) = 6.4: The largest interval is from t = -0.5 to t = 0
• y(0) = 0: The largest interval is from t = 0 to t = 5.5
• y(5.5) = -3.14: The largest interval is from t = 5.5 to t = 10
• y(10) = 2.6: The largest interval is from t = 10 to t = 74

Answer 2

6.4 I think this one's tough