Find the particular solution of this differential equation:
y`` −3y` −10y=10t2+16t−19
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?