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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(−5)=6. c=

Respuesta :

Answer:

c = 6*e^(-10) -  e^(-5)  ( ≈ -e⁻⁵ = -6.74*10⁻³)

Step-by-step explanation:

for the function

y=c*e^(−2x)+e^(−x)

as a solution of y'+2y=e^(−x)

then for  y(x=−5)=6

6 =c*e^(−2(-5))+e^(−(-5)) = c*e^10 + e^5

6 = c*e^10 + e^5

c = (6 -  e^5)/*e^10 = 6*e^(-10) -  e^(-5)

c = 6*e^(-10) -  e^(-5)  ( ≈ -e⁻⁵ = -6.74*10⁻³)

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