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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.

User Tryurbest
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1 Answer

3 votes

Answer:


c = 1190.2

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 = (2.9502)/(e^(-6))


c = 1190.2

User Keshav Vishwkarma
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