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First let me say I am very frustrated at this and could use some real through advice. My school says to not take differential equations for a BS in physics. They instead give us a real poor packet to learn it on our own with 'guidance' from a teacher. :uhh: I am wishing I took diff. eq. anyway...

[tex] y\ddot - y\dot -20 y = 17sin(3t) [/tex]

1) Find the general soltuon for homogenous

2)find particular soltuons

3)fin solution for [tex]y\dot(0) = -2[/tex], [tex] y(0) = -1[/tex]

First I need to solve the homo. part. I think I can do that.

I find the characteristic equation to be [tex] r^2 -r -20 = 0 [/tex] and get [tex] y(t) = \alpha e^(2t) + \beta e^(-t) [/tex]

I now need to find a particular solution. I have no idea how to do this. A table in my 'packet' says for inhomogeneity of C sin(wt) , the general form of [tex] y_p(t)[/tex] is [tex] A cos (\omega t) + B sin (\omega t) [/tex].

What do I do with this [tex] y_p(t)[/tex] thing? Please give me some very detailed hints on this part! Thank you.

If I can get the particular solution I think I can apply the boundary conditions.

## Homework Statement

[tex] y\ddot - y\dot -20 y = 17sin(3t) [/tex]

1) Find the general soltuon for homogenous

2)find particular soltuons

3)fin solution for [tex]y\dot(0) = -2[/tex], [tex] y(0) = -1[/tex]

## Homework Equations

## The Attempt at a Solution

First I need to solve the homo. part. I think I can do that.

I find the characteristic equation to be [tex] r^2 -r -20 = 0 [/tex] and get [tex] y(t) = \alpha e^(2t) + \beta e^(-t) [/tex]

I now need to find a particular solution. I have no idea how to do this. A table in my 'packet' says for inhomogeneity of C sin(wt) , the general form of [tex] y_p(t)[/tex] is [tex] A cos (\omega t) + B sin (\omega t) [/tex].

What do I do with this [tex] y_p(t)[/tex] thing? Please give me some very detailed hints on this part! Thank you.

If I can get the particular solution I think I can apply the boundary conditions.

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