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- Homework Statement
- Identify the homogenous solution and the particular solution. C is an arbitrary constant.

- Relevant Equations
- y(t) = C*(e^t)+((t^3)-(t^2)+5t-6)*(e^t)+((t^3)-(t^2)+5t-6)*(e^2t)

I identified the root 1 with multiplicity 1 and the root 2 with multiplicity 1. So The characteristic equation is ((m-1)^2)*(m-2)=0. Simplifying and substituting with y I found: y'''-4y''+5y'-2y=0.

So now I've realized that this is actually describing y(t)=(C1)*(e^t)+(C2)*(e^t)+(C3)*(e^2t) and I do not know how to proceed accounting for the term ((t^3)-(t^2)+5t-6) included twice. In general I don't know of another step to begin with and haven't had luck finding any instruction on how to move from a solution family to homogenous or particular solutions.

I'd appreciate some hint as to where to start; thanks!

So now I've realized that this is actually describing y(t)=(C1)*(e^t)+(C2)*(e^t)+(C3)*(e^2t) and I do not know how to proceed accounting for the term ((t^3)-(t^2)+5t-6) included twice. In general I don't know of another step to begin with and haven't had luck finding any instruction on how to move from a solution family to homogenous or particular solutions.

I'd appreciate some hint as to where to start; thanks!