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]
