contestada

The family of functions y = ce^{-2x} + e^{-x} is solution of the equation y' + 2y = e^{-x}. Find the constant c which defines the solution which also satisfies the initial condition y(3)= 3.

Respuesta :

Answer:

[tex]c = 1190.2[/tex]

Step-by-step explanation:

We have the following solution:

[tex]y(x) = ce^{-2x} + e^{-x}[/tex]

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

[tex]y(x) = ce^{-2x} + e^{-x}[/tex]

[tex]y(3) = ce^{-2*3} + e^{-3}[/tex]

[tex]3 = ce^{-6} + e^{-3}[/tex]

[tex]3 = ce^{-6} + 0.0498[/tex]

[tex]ce^{-6} = 2.9502[/tex]

[tex]c = \frac{2.9502}{e^{-6}}[/tex]

[tex]c = 1190.2[/tex]

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