Question

In each of Problems 7 through 12, state where in the ty-plane the hypotheses of Theorem 2.4 .2 are satisfied.

y'=t-y/2t+5y
y'= (1-t²-y²)¹/²

Answer 1

The hypotheses of Theorem 2.4.2 are satisfied in specific regions of the ty-plane.

Step-by-step explanation:

In each of Problems 7 through 12, Theorem 2.4.2 states the conditions in the ty-plane where the hypotheses are satisfied.

For the equation
`y' = t - y/2t + 5y` satisfied when 2t + 5y ≠ 0. This means that the function is defined for all values of t and y except when 2t + 5y = 0.

For the equation
`y' = (1 - t² - y²)¹/²`satisfied when 1 - t² - y² ≥ 0. This means that the function is defined for all values of t and y that satisfy 1 - t² - y² ≥ 0.