(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

(I am using b, for beta)

Let

[tex]f(t)=ce^{-\beta t}[/tex]

with b a fixed number and c in R is arbitrary but given.

Write the general solution of

[tex]x'=-x+f(t)=-x+ce^{-\beta t}[/tex]

Hint: Use undetermined coeff. and consider a particular solution of the form

[tex]x_p=\alpha e^{-\beta t}[/tex]

and determine [tex]\alpha[/tex]

2. Relevant equations

3. The attempt at a solution

I have solved for

[tex]\alpha = \frac{c}{-\beta +1}[/tex]

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# Homework Help: Undetermined Coeff.

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