Hello,

I'm stumbling on an example for finding the particular solution to a difference equation. I have:

$\displaystyle y'(t) - 3y(t) = t^2u(t) : y(0) = 2$

So I understand that one way to solve this is by finding the homogenous solution in terms of unknown integration constants, then finding the particular solution. I've figured out the homogenous solution to be

$\displaystyle Ae^tu(t)$

But I'm tripping on the particular solution. Stroud's book 'Advanced Engineering Mathematics' states that if the right hand side of the original difference equation has a polynomial term $\displaystyle t^n$ then the particular solution should be in the form

$\displaystyle C_{n+1}t^{n+1} + C_nt^n + C_{n-1}t^{n-1} + ... + C_0$

So I take this that the particular solution should be of the form

$\displaystyle Ct^3 + Dt^2 + Et + F$

However in Stroud's example for $\displaystyle n^2$ he gives

$\displaystyle Cn^2 + Dn + E$

Have I misunderstood or has he made a mistake?

Thanks!