Finding Particular Solutions for Second Order Linear Differential Equations

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SUMMARY

The discussion centers on finding a particular solution for the second-order linear differential equation y'' + 2y' + 5y = 4(e^-t)cos2t. The initial attempt at a particular solution, y.p = At(e^-t)cos2t + Bt(e^-t)sin2t, was unsuccessful. After further analysis and assistance from forum members, the user resolved the issue with their approach, confirming the importance of correctly substituting the proposed solution back into the original equation.

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Homework Statement



Find particular solution for
y''+2y'+5y = 4(e^-t)cos2t

Homework Equations



y.c = C(e^-t)cos2t + C(e^-t)sin2t

The Attempt at a Solution



y.p (particular solution) = At(e^-t)cos2t + Bt(e^-t)sin2t does not work! Help please!
 
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Are you sure your y_p doesn't work? Why don't you show us what you're getting when you plug it into the ODE.
 
Last edited:
reply oh i figured it out. thank you!
 

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