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Find all values of m so that the function y = emx is a solution of the given differential equation. (enter your answers as a comma-separated list.) y' + 6y = 0

Respuesta :

LammettHash
[tex]y=e^{mx}\implies y'=me^{mx}[/tex]

[tex]y'+6y=0\iff me^{mx}+6e^{mx}=(m+6)e^{mx}=0\implies m=-6[/tex]

So one solution to the ODE is [tex]y=e^{-6x}[/tex].

Answer:

m = -6

Step-by-step explanation:

Suppose we have an differential equation in the following format:

ay' + by = 0

The differential equation has the following equivalent polynomial

ar + b = 0.

The root of the polynomial is a value of m so that the function y = e^(my) is a solution of the equations.

In this problem, we have that:

y' + 6y = 0

The polynomial is

r + 6 = 0

r = -6

So the value is m = -6

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