Question

4) Discuss clearly the existence of solutions to the following IVP using the Uniqueness Theorem a) $y' = (y - 2)^{1/2}$ $y(0) = 2$ b) $y' = (y - 2)^{-1/2}$ $y(0) = 2$ c) $y' = (y - 2)^{3/2}$ $y(0) = 2$

          4)
Discuss clearly the existence of solutions to the
following IVP using the Uniqueness
Theorem
a) $y' = (y - 2)^{1/2}$  $y(0) = 2$
b) $y' = (y - 2)^{-1/2}$ $y(0) = 2$
c) $y' = (y - 2)^{3/2}$  $y(0) = 2$

Added by Jose Ramon W.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Emily Anderson

Step 1

To apply the Uniqueness Theorem, we need to check if the function f(x, y) = (y - 2)^(1/2) is continuous and satisfies the Lipschitz condition in a neighborhood of the initial condition (0, 2). First, let's check if f(x, y) = (y - 2)^(1/2) is continuous. Since Show more…

Show all steps

Thanks for your feedback!

I need help, please, as soon as possible. It's differential equations. 4) Discuss clearly the existence of solutions to the following IVP using the Uniqueness Theorem: a) y' = (y - 2)^(1/2), y(0) = 2 b) y' = (y - 2)^(-1/2), y(0) = 2 c) y' = (y - 23/2), y(0) = 2