- #1

yaro99

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## Homework Statement

y''+3y'+3.25=3cost-1.5sint

## Homework Equations

y

_{h}= e

^{(a/2)t}(Acost+Bsint)

y

_{p}= Kcos(ωt)+Msin(ωt) [when r(x)=kcos(ωt) or ksin(ωt)]

## The Attempt at a Solution

I got the homogeneous solution, which is e

^{-1.5t}(Acost+Bsint)

but I am having trouble with the particular solution.

I tried the above equation, making y

_{p}=K

_{1}cos(ωt)+M

_{1}sin(ωt)+K

_{2}cos(ωt)+M

_{2}sin(ωt)

since there are 2 trig functions as r(t).

I couldn't solve for the variables by plugging into the original equation because I was left with 4 variables and only 2 equations.

EDIT: realized I wasn't consistent with my independent variable, made them all t's instead of t's and x's

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