Second order, inhomogeneous ODE, solve for particular integral

[themathlete]

hi, can anyone solve 5y′′+3y′+25y=−61sin(2t) to give a particular integral in the form yPI(t)=acos(ωt)+bsin(ωt)? would be much appreciated

 

[Deleted member 4993]

hi, can anyone solve 5y′′+3y′+25y=−61sin(2t) to give a particular integral in the form yPI(t)=acos(ωt)+bsin(ωt)? would be much appreciated

What are your thoughts?

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Hints:

Start with

y = A*cos(2t) + B*sin(2t)

y' = 2[-A*sin(2t) + B*cos(2t)]

y" = -4*[A*cos(2t) + B*sin(2t)]

Now put these into your DE and solve for A and B by collecting similar terms.