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3 years ago

SOLVE. y''+3y'+2y=4e^x

1 answer:

8 0

This a second order linear differential equation with the solution given by the general solution + the particular solution.
The general solution is given by Ae^mx + Be^nx; where m and n are solutions to the quadratic equation t^2 + 3t + 2 = 0
(t + 1)(t + 2) = 0
t = -1 or t = -2
general solution = Ae^(-x) + Be^(-2x)
For the particular solution, Ce^x + 3Ce^x + 2Ce^x = 4e^x
6Ce^x = 4e^x
C = 4/6 = 2/3

Therefore, solution is y = Ae^(-x) + Be^(-2x) + 2/3e^x

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<h3>How to write an expression for the total cost?</h3>

In this exercise, you're required to write an expression for the total cost of the daycare for Lucy's dog this week. Thus, we would assign a variable to the cost for full-day and half-day day care as follows:

Let the cost for full-day be F.

Let the cost for half-day be H.

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Read more on expressions here: brainly.com/question/12189823

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