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## Homework Statement

Find the particular solution of this differential equation:

y`` −3y` −10y=10t

^{2}+16t−19

## Homework Equations

## The Attempt at a Solution

I'm not really sure what the roots look like for 10t^2 + 16t - 19. I thought t had roots (0,0). Does that mean t^2 has roots (0,0,0)? And -19 has no roots? So the roots of the entire right hand side is (0, 0, 0, 0, 0)?

And yp = at + bt^2 + ct^3 + dt^4 + et^5?