# Second order nonhomogeneous ODE

yaro99

## Homework Statement

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

## Homework Equations

yh = e(a/2)t(Acost+Bsint)
yp = 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 yp=K1cos(ωt)+M1sin(ωt)+K2cos(ωt)+M2sin(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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