family of solutions of the second-order DE y y 0. Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions. 12. y(1) 0, y(1) e

Step-by-step explanation:

Given

Required

The solution

Differentiate

Next, we solve for c1 and c2

implies that; x = 1 and y = 0

So, we have:

--- (1)

implies that: x = 1 and y' = e

So, we have:

--- (2)

Add (1) and (2)

Divide both sided by e

Divide both sides by 2

Substitute in

Rewrite as:

Multiply both sides by e

So, we have:

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step-by-step explanation:

step-by-step explanation:

ok one would be money, and the other would be refreshments or something similar. if each bag of popcorn is 5.00 and each drink is half of that that means drinks are 2.50 the proper way to do that would to look and see how much of each you can buy without exceeding a limit of 30.00