Find a particular solution for a non-homogeneous differential equation

  • Thread starter blouqu6
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Find a particular solution for the following equation:

y"+2y'+y=12.5e-t

I'm not sure on which method to use. Here's my attempt using the undetermined coefficients method:

→y"+2y'+y=12.5e-t
r2+2r+1=0
r=-1 *not even sure if this part is useful

→yp=e-t
yp'=-e-t
yp"=e-t

→y"+2y'+y=12.5e-t
(e-t)+2(-e-t)+(e-t)=12.5e-t

e-t(1-2+1)=e-t(12.5)

This is where I get stuck; I don't believe I'm taking the right approach from the get-go. Any help would be greatly appreciated.

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  • #2
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Find a particular solution for the following equation:

y"+2y'+y=12.5e-t

I'm not sure on which method to use. Here's my attempt using the undetermined coefficients method:

→y"+2y'+y=12.5e-t
r2+2r+1=0
r=-1 *not even sure if this part is useful
It's very useful, as it gives you the complementary solution, the solution to the homogeneous problem. Note that r = -1 is a repeated solution of the characteristic equation.
→yp=e-t
Not a good choice for a particular solution. e-t is a solution of the homogeneous problem, so can't possibly be a solution of the nonhomogeneous problem.
yp'=-e-t
yp"=e-t

→y"+2y'+y=12.5e-t
(e-t)+2(-e-t)+(e-t)=12.5e-t

e-t(1-2+1)=e-t(12.5)

This is where I get stuck; I don't believe I'm taking the right approach from the get-go. Any help would be greatly appreciated.

Homework Statement





Homework Equations





The Attempt at a Solution

 

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