Question

Determine (without solving the problem) an interval in which the solution of the given initial value problem is certain to exist, (1 - 2)y' + (Int)y = 71, y(1) = 7 ! i

Answer 1

The solution of the given initial value problem is certain to exist for all values of x in the interval (-∞, +∞).

Step-by-step explanation:

To determine an interval in which the solution of the given initial value problem is certain to exist, we need to consider the conditions that ensure the problem is well-posed. In this case, the given initial value problem is in the form (1 - 2)y' + (Int)y = 71, y(1) = 7. The key factor to consider is the coefficient of the derivative term, which is 1 - 2 = -1. Since the coefficient is negative, the initial value problem is guaranteed to have a unique solution. Therefore, we can conclude that the solution of the given initial value problem is certain to exist for all values of x in the interval (-∞, +∞).