Particular solution form for -2y''+y'+y=2t^2-2t-5e^(-2t)

[hard_assteel]

For this nonhomogeneous differential equation:

-2y''+y'+y=2t^2-2t-5e^(-2t)

would the setup for the particular solution (yp) be;
Ae^(-2t)+Bt^2+Ct+D?

Thank You

 

[Mark44]

It depends on the solutions to the homogeneous problem.

What are the solutions to -2y'' + y' +y = 0?

Or, equivalently, 2y'' - y' - y = 0?

If the roots of the characteristic equation for the homogeneous equation aren't r = 0 or r = -2, then, yes, that's what you want for your particular solution.

 

[hard_assteel]

the roots are -.5 and 1

 

[djeitnstine]

Edit, nevermind I think its fine