I'm stuck on just one problem.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

2y'' + 3y' + y = t^{2}+ 3sin(t)

2. Relevant equations

It says in the lesson that if you have a polynomial, guess a solution is

"Y_{i}(t)= T^{s}(A_{0}t^{n}+ A_{1}t^{n-1}+ .......... + A_{n})

where s is the smallest nonnegative integer (s=0,1, or 2) that will ensure that no terms in Y_{i}(t) is a solution of the corresponding homogeneous equation."

And I don't really understand that jargon. Maybe someone could dumb it down for me.

3. The attempt at a solution

Since the solution is the sum of two different functions, t^{2}and 3sin(t), I can solve the differential equation for each individually, and them add them together at the end since the sum of the solutions to a differential equation is also a solution.

I got the solution to

2y'' + 3y' + y = 3sin(t).

It is Y_{1}(t) = (-3/10)sin(t) -(9/10)cos(t)

But Y_{2}(t) is giving me trouble.

I guessed Y_{2}(t) = A_{0}t^{2}+ A_{1}t + A_{2}but ended up with a system equations that still had t in it; thus I couldn't solve it.

Set me on the right track.

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# Homework Help: Nonhomogeneous Equations; Method of Undetermined Coefficient

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