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Rudiy27
2 years ago
7

The family of functions y = ce^{-2x} + e^{-x} is solution of the equation y' + 2y = e^{-x}. Find the constant c which defines th

e solution which also satisfies the initial condition y(3)= 3.
Mathematics
1 answer:
Rufina [12.5K]2 years ago
4 0

Answer:

c = 1190.2

Step-by-step explanation:

We have the following solution:

y(x) = ce^{-2x} + e^{-x}

We want to find the value of x that satisfies the following condition:

y(3) = 3.

This means that when x = 3, y = 3. So

y(x) = ce^{-2x} + e^{-x}

y(3) = ce^{-2*3} + e^{-3}

3 = ce^{-6} + e^{-3}

3 = ce^{-6} + 0.0498

ce^{-6} = 2.9502

c = \frac{2.9502}{e^{-6}}

c = 1190.2

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